You could sue them in Small Claims court for failing to provide you with the credited card, but it seems this can probably be resolved without litigation. Have you escalated the issue and asked to speak to a supervisor, then that supervisor's supervisor? Don't waste your time with underlings, get to someone with authority to fix this.
To prepare, look up the company on your state's Secretary fo State website, find out who their agent for service of process is, and tell whoever you speak with that if you don't have this resolved immediately, you'll sue, and let them know you know who their agent for SOP is and that you're prepared to sue if necessary.
I'm only licensed in CA. Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.