Billing Cycle:Customer billing cycles also control how long it takes to receive news of a credit card refund. For example, if you have an account that ends on the 29th day of each month, you may receive your card statement on the 5th day of the next month.imeline:According to the TaxAct website, credit card refunds can take anywhere from two to 30 days before they are complete. The first 24 to 48 hours of this period involve the initial refund with the credit card company.