This is a hard (if not impossible question to answer, seeing that many early films have been lost in fires etc.) but I will try point you in the right direction. Seeing as dialog is a factor in your question the film must have been made after 1927, when the jazz singer was announced as the first "talkie".
Then we have a span of 11 years where the movie you are looking for could have been made until 1938 when HUAC (House Un-American Activities Committee) released a report on communist activities in Hollywood and started the HUAC-hearings. We can not be sure, but there was propably no features during this period with russian (or russian speaking) actors. After that period I know of a movie made in 1966 whit a serbian actor speaking russian, Milos Milos in The Russians Are Coming, the Russians Are Coming directed by Norman Jewison, but I have a hard time thinking this would be the fist one.
Also, it is likley that if such a movie was made during the HUAC-hearings it might have been an independent production and hard to track.
I hope this information will be of help.