It's certainly an unusual policy, but every doctor's office has it's policies and procedures.  Some don't honor BCBS and other's don't handle worker's comp.  They are a private business, so they have the right to set up rules for the operation of their business, and you have the right to refuse those rules and go somewhere else.  Even though a bit odd-- and not very customer savvy-- the requirement for a credit card number is not per se an illegal practice as a prerequisite to an appointment.