I've heard that he was not. Latter I've heard that he would have joined the fray if not because of political consideration.
I forgot the source.
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.
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.
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 ...
EDIT: as so well expounded in the other answer, the non-antisemitism of Rommel was relative, i.e., compared to the rest of Germany he appeared to be 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.