Unfortunately, it's very hard to hold a credit-card company liable for damages caused by their screw-up. If you were able to get out of paying the bills on this bogus card, and it's not showing up on your credit report, then it's unlikely you have enough damages to make it worth suing. If you incurred any particular large expense as a result of the bogus card, you might discuss the matter with a consumer attorney. For example, if charges on the bogus card showed up on your credit report and caused other loans to go into default or switch to a higher interest rate, it might be worth a lawsuit. But if you just had to spend 40 hours of your own time sorting this out and dealing with incompetent customer-service people on the phone, well, thanks for your contribution to the credit-card company's bottom line! Your free labor is the engine that drives our economy!
You could possibly sue for negligence, but would need to prove you suffered damages as a direct result of the wrongful issuance of the credit card in your name.
I would need to know much more about what happened in order to give you a better response.
PLEASE NOTE THAT THIS RESPONSE SHOULD NOT BE CONSTRUED AS A LEGAL OPINION OR ADVISE, AND DOES NOT CREATE AN ATTORNEY-CLIENT RELATIONSHIP. IN ORDER TO RENDER A LEGAL OPINION OR ADVISE, THE RESPONDING ATTORNEY WOULD NEED FAR MORE INFORMATION THAN HAS BEEN PROVIDED, AND WOULD NEED TO BE RETAINED PURSUANT TO A WRITTEN FEE AGREEMENT.
California has a very good identity theft statute that includes a statutory damage of up to $30,000 if a creditor fails to properly investigate a consumer's claim on identity theft.
You should consult with an experienced consumer attorney.