Legal Question in Criminal Law in California

Yes, unless you have a contract with the company that says it can't. That's unlikely.

Most employees are "at-will," which means they can be fired for any legal reason -- or for no reason at all. Even where the employer is constrained by a contract, a good-faith belief that the employee committed a crime is usually valid reason to fire him. That's true even if the crime was committed elsewhere on his own time.