There is a brief discussion by u/finalnsk about a similar topic here, so I shall attempt to delve into the matter a bit more here. Note that it is somewhat difficult to pinpoint if Stalin (or indeed any intelligence organ of the USSR for that matter) knew the specifics of Pearl Harbor, but Richard Sorge did reassure the NKVD and by extension the Red Army (unfortunately to limited effect) about the fact that Japan was looking elsewhere for its warpath. Let's begin.

Note: All the information in this response comes from Owen Matthews' excellent biography An Impeccable Spy, on the life of Richard Sorge, who was Stalin's chief informant in Japan before and during the war until his capture in 1941.

Firstly, the origins of this claim are actually even more deeply rooted in Cold War paranoia than actual historical sources. In the wake of the Japanese surrender and US Occupation the life of Richard Sorge, who had so successfully established a spy ring with members in some of the highest echelons of the Japanese government, came to full attention. The fear which General MacArthur and other high-ranking US officials had was that there were "Sorges" operating in America. To that end, MacArthur assigned to General Charles Willoughby the task of combing the Japanese judicial records of Sorge's spy ring's activities, in the hopes of uncovering potential leads to Soviet spy rings in the USA. These findings became a key focus during the "Red Scare" period of the early 50s, as the House of Representatives Un-American Activities Committee (led by Senator Joseph McCarthy) sought to find clues of Soviet involvement in "encouraging Japan to attack Pearl Harbor." After Willoughby himself testified that "Stalin did get the information [about Pearl Harbour]", Owen Matthews describes the 'Pearl Harbor-Kremlin Conspiracy" thereafter:

"[T]he myth that the Soviets knew of Japan's plans for a surprise attack and failed to warn their allies in Washington of the danger was off and running. Senator Adlai Stevenson spoke of Stalin's 'duplicity' over Pearl Harbor. Several books were written claiming that the Japanese attack on the US was a plot orchestrated by the Kremlin to defuse the danger to Siberia."

Such conspiracies and claims were entirely false: Sorge did not know of Pearl Harbor. What he did know however, was that Japan was going to attack America. He signalled as such in a dispatch to Centre (the codename for intelligence headquarters back in Moscow) in a telegram, based on information off of close friend (and confidant) Admiral Paul Wenneker (who was the German naval attache to Tokyo). The dispatch is as follows (dated 14th September, 1940):

"Navy friends of PAUL [Wenneker's rather flimsy codename] say that war against USSR is no longer being discussed. The sailors no longer believe in the possibility of success talks between Konoe [Japanese PM] and Roosevelt. Preparing for attack on Thailand and Borneo he thinks that Manila must be taken [as a staging post]. That means war with America."

These "prophetic" words, as Matthews himself calls them, would all come true within a year, and it gave the Kremlin reassurance that their Far Eastern units were not going to be facing Japanese troops anytime soon.

So to answer your question: there is no evidence to support the theory that Sorge and/or Stalin knew of Pearl Harbor. What there is proof of, is the fact that Sorge was supplying Stalin with information that America would eventually come to blows against Japan, but how? remained a question that neither would discover until the surprise attack on December 7th. Hope this helps answer your question, and feel free to ask any follow-ups!