I've heard that he was not. Later, I've heard that he would have joined the fray if not because of political consideration.
I forgot the source.
I am not sure what you mean by "joined the fray", but it does appear that Rommel did not share Hitler's antisemitism despite being relatively close to him throughout the 1930-ies. Rommel admired Hitler for his success in dismantling the Versailles regime, but ...
During Rommel's time in France, Hitler ordered him to deport the country's Jewish population; Rommel disobeyed. Several times he wrote letters protesting against the treatment of the Jews. He also refused to comply with Hitler's order to execute Jewish POWs.
EDIT: as so well expounded in the other answer, the non-antisemitism of Rommel was relative, i.e., compared to the rest of Germany (e.g., Manstein) he appeared to be a gentleman - while serving the Nazi regime.
In the absolute terms one can say with confidence that due to Rommel's actions (his successes on the battlefield) the war lasted longer and many more innocents (Jews, Gypsies, Russians, Poles &c) were murdered. It does appear that these deaths were not to his liking, but they did happen.
All of Western European culture, world-wide, was anti-Semitic at that time. Germany itself was extremely anti-Semitic, even more so than Europe as a whole. I do not hesitate to state that even that handful of Germans who risked their lives to save Jewish friends, would have to be regarded as anti-Semitic in regard to Jews who were not personally well-known to them.
However, what the Nazis' engaged in went far beyond every-day anti-Semitism. So far past everyday anti-Semitism that it gave anti-Semitism itself a bad name, so that it became unfashionable for the first time in over a millennium. Permanently unfashionable.
The movie A Gentlemen's Agreement could not have been made in 1937. Jewish refugee ships were still being refused entry to Montreal and New York and even Haifa. But by 1947, with the horrors of the Holocaust really starting to sink in, it almost had to be made.
So in this context, I think it is necessary to say "Of course Rommel was anti-Semitic - all of Germany was. All of North America was." However, there is a world of difference between run-of-the-mill anti-Semitism and support of the Holocaust.
I cannot truly be 100% certain that on an anti-Semitism scale of 1 to 10,000, where Hitler rates a 9,999.9 and a 0 rating is earned only by someone who can vote on his club membership without the slightest thought of religion, that Rommel isn't a 0.
However in a world and time where even Churchill and FDR were more likely to rate 100 or so than 0, it is almost impossible to believe that Rommel was a 0. Being a tiny bit anti-Semitic; a little too complacent in the anti-Semitism of one's colleagues; a little too eager to laugh at a Jewish joke if only to hide one's own Italian, or Irish, or Spanish, or Polish, or Dutch, or Balkan, or Catholic, or Baptist, or Orthodox, or other heritage; was just too easy. It was very difficult, and conspicuous, to rate a 0 in those times; and for an ambitious general in Nazi Germany looking to make his reputation in a world war, not being just a tiny bit anti-Semitic, passively, almost seems too much to ask.
In this context, I find the question almost unfair. It really should not attempt to look into the deepest recesses of Rommel's heart to judge the presence or absence of anti-Semitism. It should rather confine itself to solid evidence on his actions in regards to Jews, and judge him on this basis alone: To what extent was he willing to stand up and obstruct the Nazi extermination of the Jews, at risk to life, limb, prosperity and family.
Rommel was not an anti-semite, but he did approve of Hitler's plans to strengthen the military and use military might. He wrote a letter to Hitler saying "this business with the Jews has to stop". When Hitler disregarded his plea, Rommel tried to save Jews from camps by suggesting to Hitler that they be taken into the army.
This prompted Hitler to remark: "That man has no idea what we are trying to accomplish".
Question: Was Rommel anti-semetic?
Absolutely, no question. Rommel was a high ranking general and a personal friend of Hitler. He was an early Hitler admirer, who served as Hitler's personal body guard and came into contact with many of the highest ranking Nazi's. He had both personal and military information and meetings on the liquidation of Jewish populations. There is no question that he knew about the Nazi's controversal policies. The only question is how anti-semitic was he.
While the extent of Rommel’s antisemitism is difficult to quantify. Best case he ignored the Nazi's racial puriity / liquidation policies. It is accurate that he refused to cary out several orders to execute POW's. Black and Jewish POW's in North Africa, and Free French fighters in occupied France. This however does not excuse his knowledge, silence and aid in other liquefaction exercises.
In North Africa Rommel held meetings with Walther Rauff to propose Schutzstaffel (SS) paramilitary death squads for when Egypt fell. Rauff was the inventor of gas vans which operated and murdered civilians in Rommel's sectors. Rauff coordinated his actions with Rommel's staff. We don't know what Rommel thought about the murder of helpless civilians in his armies sphere of control, but their is no question that Rommel knew about these actions, was complicite both in the planning and acts.