In Anne Applebaum's recent book Iron Curtain: The Crushing of Eastern Europe 1944-1956, she claims the USSR supported the new state of Israel and states
Stalin believed Israel would quickly join the communist camp.
She doesn't cite any references for this, but is it true? And if so, what grounds were there for Stalin believing Israel would align itself with the Soviet Union?
It is clear that Stalin supported the creation of Israel. From the Wiki:
For Soviet foreign policy decision-makers, pragmatism took precedence over ideology. Without changing its official anti-Zionist stance, from late 1944, until 1948 and even later, Joseph Stalin adopted a pro-Zionist foreign policy, apparently believing that the new country would be socialist and would accelerate the decline of British influence in the Middle East.[cite: Paul Johnson, A History of the Jews (1987) p.527]
On May 17, 1948, three days after Israel declared independence, the Soviet Union legally recognized it de jure, becoming the first country to grant de jure recognition to the Jewish state..In addition to the diplomatic support, arms from Czechoslovakia, part of the Soviet bloc, were crucial to Israel in the 1948 Arab-Israeli War.
It's quite clear that this would NOT have happened had Stalin disagreed.
As far as " what grounds were there for Stalin believing Israel would align itself with the Soviet Union":
as the commenters noted, most of the early Zionists and founders of Israel were politically quite left and socialist-bent. I consider this fact to be too well known and trivial to bother with sites, but if you wish I'll add them. Ex: [1].
Also, at the time, British and the West in general started swinging towards being more pro-Arab due to geopolitical concerns, notably oil (Lawrence of Arabia being a good example; and British resistance to the creation of Israel despite Balfour commitments being another example). As such, Israel would be a natural counterweight for Stalin to extend his influence in Near East, the same way United States was using Israel once the geopolitical alignments reversed themselves in 1970s when Arab states became Soviet clients and Israel American one.
Stalin was an ideologue, but not a very rigid one, and he was not an idiot.
He supported Israel because it was a thorn in the side of the British Empire (and its Arab relationships), not because the Zionists were left wing.
After all, left wing or right wing, anyone who did not toe the Moscow's line precisely was an enemy (cf Tito-Stalin Split). Stalin knew full well that people neither join the communist camp nor enter the prison camp voluntarily, and did not expect Israel to do so; and he did not have the resources or reach to turn Israel into another Poland or Romania.
Stalin probably didn't believe that Israel would go "Communist," because there was no ideological connection between Communism and Zionism (except that a few people were in both camps).
Stalin probably believed that Israel could become his "catspaw" in the Middle East. The reasoning would be "the enemy of my enemy is my friend."
Stalin did not treat Jews particularly well in the Soviet Union. For all that, the Soviet Union deserves a lot of credit for the defeat of Nazi Germany, the persecutor of the Jews. Stalin was hoping that some of that "credit" would "rub off" on Jews and Israelis.
Stalin and the Soviet Union feared the Moslems, particularly the Arabs. The Israelis were the natural enemies of the Arabs. Stalin hoped (with reason) that the Israelis could keep the Arabs tied up on the Middle East, diminishing their threat to the Soviet Union.
Basically, there was some reason to hope that the Soviet Union and Israel could become "fellow travelers," not "fellow ideologues."
Stalin was hoping that Israel became socialist. The reasons being was:
There was mass emigration to Israel after WW2. Many Soviet Jews left the USSR to go to Israel. Stalin hoped that the Jews that had left, still maintained some loyalty to the USSR.
Since the West did little to rescue Jews from persecution of the Nazi's, Stalin assumed that while his persecution of the Jews was not as great as Nazi's that the Jews would favor his regime. Stalin thought Jews had some resentment to Britain for doing little to allow them to come in before WW2. Stalin on the other hand, persecuted everyone no matter their nationality.
The Soviet Union did allow some German exiled Jews to enter during the war and continue their religious activities.
USSR wanted an opportunity to gain a foothold, and spread socialism in the Middle East and Africa since Europe was blocked off with the heavy presence of NATO.
Soviet Union wanted revenge for the Iran 1946 crisis
Soviet Union was on a mission to overthrow capitalism after WW2.
https://en.wikipedia.org/wiki/Israel%E2%80%93Russia_relations
https://en.wikipedia.org/wiki/Iron_Curtain
Geopolitics
It is important to point out that Stalin's support for Israel had not necessarily be ideological, but rather a question of geopolitics. The Soviet Union did vote for the UN partition plan, and was quick to recognize the newly proclaimed state of Israel (as has been pointed in the answer by @DVK). In this sense the Soviet policy was mirroring the American one, and likely reflected the rivalry of the two nations for the domination in the Middle East. Both nations were quick to adopt a detached position, and impose embargoes on Israel - the US modern friendly stance dating back to mid-sixties, when it became obvious that Israel was going to survive and likely become a dominant force in the Middle East. Israel in its early years relied mainly on the support of UK and France, whereas the Soviet initially pro-Israeli stance was quickly followed by persecution of Jews (see Doctor's plot and Jewish Anti-fascist Committee) which failed to reach significant proportions due to the Stalin's death. The USSR further adopted policies histile to Israel, Jews, and Jewish migration to Israel all the way to its collapse.
Ideology
Many of the early Zionists and the Israel's founding fathers held strongly socialist views, and Israel itself was a heavily socialist country till the economic liberalization in 80s. Kibbutzim has been arguably the most successful implementation of communist ideas. Yet, it is also necessary to point out that, as a view on Jewish emancipation, Zionism was in opposition to Socialists/Communists, who believed in the emancipation of European Jewery via social transformation and abolition of ethnic/social/religious distinctions, rather than via creation of a state. Thus, Stalin probably had no illusions about the impossibility of Israel becoming communist.
On the other hand, USSR had a long story of framing its support for nationalist/liberation movements in ideological terms, see, e.g., Arab socialism and Soviet support for Kurds .
Stalin did not care about Israel.
Author Odd Arne Westad "The Cold War" A world history (2019) argues
In some cases the Soviet Union seemed more preoccupied with acting as a spoiler to US or British interests than developing a long term policy of its own. The Soviet recognition of Israel is a case in point. In spite of its own deep-seated and escalating anti-Semitism, Stalin believed that is was more important to create difficulties for Britain's position in the middle east, than to stick with the earlier Soviet policy of creating a secular unified state in Palestine (Westad, 156)
Source:
Marxism and Communism were invented by people of the Jewish tribe. I use the word 'tribe' instead of Jewish 'faith' since atheism would contradict the tenants of Judaic faith so a Jewish atheist may be an oxymoron. Karl Marx, the co-author of Das Capital and Communist Manifesto was of Jewish ancestry with both his maternal and paternal grandfathers being rabbis. Leon Trotsky, whose original name was Lev Davidovich Bronstein, was born from Jewish parents.
Karl Marx formed the ideology of communism and Trotsky its implementation in the October Bolshevik revolution of Russia in 1917. Trotsky was founder and commander of the red army and his efforts were critical for both the victories of the revolution and the Russian civil war (1918-1923).
The communist revolution liberated Soviet Jews from the ghettos and allowed them to flourish in administrative, academic, and scientific posts in the Soviet state. While Stalin himself was not of Jewish ancestry, much of his cabinet, advisers, and top administrators were of Jewish extraction. Since communism's ideology, implementation, and administration were much carried out by people of Jewish extraction, it was only natural for Stalin to assume the Jewish state would be a communist or socialist one.
If Hitler's war against the Jew was to succeed, then he had to invade the Soviet Union where Jewish dominance in state administration prevailed. Most of the Jewish refugees immigrating into Palestine were from the communist countries of eastern Europe and the Soviet Union, a direct result of the Nazi invasion.
While the Arab population of Palestine was tolerant up to a certain point for small numbers of refugees, the sudden huge influx crossed this reasonable and tolerable threshold. The Arab nations were either British or French colonies. By supporting Israel to cause a successful implementation of socialist state, Stalin hoped to inspire socialist or communist revolutions in the Arab states to overthrow their colonial puppet governments.
Jewish intellectuals in the west were also socialists such as Albert Einstein and Robert Oppenheimer. Einstein was quoted as saying capitalism is economic anarchy. The Rosenberg spy couple who compromised US advantage in nuclear weapons technology to the Soviets and then executed were Jewish. Since many top intellectuals in the west were Jewish and socialist, Stalin, by supporting Israel hoped to at least strengthen the premise of ideological superiority of Marxism over capitalism in western debates, and cause intellectual dissension in western capitalist establishments.
The Bolshevik revolution like the formation of Israel was financed by Wall Street and western Jewish bankers and financiers. Before the Bolshevik revolution most of Russian capital was not Jewish (Gentile) in the ownership of the czar or the church. After the revolution, much of the czar's and the church's gold and other wealth was looted by the Bolsheviks. The western Jewish capital wanted to annihilate the Gentile Russian capital and aristocracy. This was payback after centuries of czarist persecution and pogroms against the Russian Jewish population.
By supporting and recognizing Israel, Stalin wanted to continue this war between the Jewish and Gentile capital as a divide and conquer strategy.
