Legal Question in Business Law in California

Not sure of legality but I would not do it. Have them charge a specific amount and then go someplace else

It is a violation of their agreements with, at least, MasterCard and Visa, for merchants to ask for photo identification in connection with the use of the cards. The credit card alone is all that can be required. In the sense that the Mastercard and Visa merchant contract is private law, it would be against the law for one of their merchants to ask for an ID at all. If this happens, you should report this violation to your card issuer. From the consumer perspective, because identity theft is so common, it is not a good idea to let others handle or copy your driver's license (or record the number, for that matter). It is intended to be used by law enforcement, not businesses.