Shaw first appeared in a short in 1932 called The Yacht Party as an uncredited orchestra member. He made three shorts with his band in 1939 and recorded the soundtrack toThe Dancing Co-Ed that same year.
Here's Artie Shaw, in Tom Nolan's Three Chords for Beauty's Sake: The Life of Artie Shaw:
I took that picture on the proviso that I would be able to rewrite any language they put in my mouth; I'm playing 'Artie Shaw' again, in a fictional situation. So, you know, I was working with people I knew. We were supposed to have John Garfield, and it was gonna be a serious story about a young trumpet player.
Anyway—Boris Morros, the producer, didn't get along with Jack Warner, and Jack Warner rescinded his deal to lend us Garfield. So we didn't have a star!
So uh—out friend Borris Morros, comes over to the Chateau Marmont, where we were working—says I got a staah!' We says, 'Who you got?' 'Fred Astaire.' I said, 'Wait a minute! This is a serious story about a trumpet player!' 'So you'll change the story.' Well, at that point—that's the last movie I ever did, the last movie I ever would do."
Here's the entire film. Interestingly, Shaw had virtually no on-camera chemistry, and his acting ability was wooden at best. It's also probably Astaire's worst film. The music, however, was a different matter. Thanks to Greg Lee for reminding me of the film: