Arnold Schwarzenegger's Son Joseph's Acting Career Taking Off

Arnold Schwarzenegger's son already follows in his dad's footsteps when it comes to bodybuilding ... but now he's mimicking his pops in Hollywood.

Sources close to Joseph Baena tell TMZ ... on the heels of landing his first big acting gig earlier this year -- in the John Malkovich sci-fi flick, "The Chariot" -- he's hired a manager, Henry Penzi, and is booking more and more roles.

We're told Joseph just finished shooting an independent film called "Bully High" -- that's where these photos are from -- where he plays the school president ... one of the main characters. "Bully High" is directed by Bill McAdams Jr.

On top of that, our sources say Baena's set to appear in an upcoming project with Bruce Willis and another project with Cartoon Network. We're told there's lots of interest in booking him for other gigs, too.

Along with Joseph's professional life taking off in 2021, it's also been a big year personally. As we previously reported ... he was seen publicly hanging out with his half-brother, Patrick, for the first time in April.