Legal Question in Business Law in California

Yes

You have (at least) three possible "causes of action" (legal theories of suit) that you might pursue.

First, and perhaps simplest, if you have a written or even an oral agreement with the client for the creation of this design, and haven't been paid the contract price, you can sue for breach of contract. If the amount is less than $7,500, you could bring the suit in small claims court.

Next, California allows a suit for common-law infringement of copyright to be brought in state courts. This could be a fall-back or alternative cause of action. Such claims are subject to a defense of "Federal pre-emption" and if used, should be drawn up by a lawyer who has taken the time to learn what facts must be plead to qualify the case for state jurisdiction. The fact that there was a contract should be helpful.

Finally, a cause of action for copyright infringement in Federal court would be a possibility, provided there has been a successful copyright application and the plaintiff (you) holds the copyright.

Other claims or causes of action might be possible or even desirable, depending upon the specifics of your relationship with the client and what happened, You should consider the amount of damages and the proof of those damages (and your chances of collecting) in deciding what kind of suit, if any, is worth while.