Can charges be made via the API using credit card information previously entered in the Payeezy Gateway Application?

I have a client who has been using the Payeezy Gateway site to charge customers for frequent orders. They enter the credit card information once, and then process all future invoices using the stored card number (similar to an auto-pay approach). Is there a way in the API to charge one of these stored credit cards / customer accounts? We'd like to automate this process for them so they don't have to manually log into the gateway to charge each and every invoice.

Thanks!