This question was put to the Standing Committee, who replied:
If the credit card is as described, then it is a new kind of riba-based transaction and of consuming people’s wealth unlawfully, making them fall into sin and contaminating their earnings and dealings. It comes under the same rulings as the riba of the Jaahiliyyah which is forbidden in sharee’ah. (Either you pay it off at the appointed time or you increase the amount). Hence it is not permissible to issue such cards or to use them. And Allaah is the Source of strength. May Allaah send blessings and peace upon our Prophet Muhammad and his family and companions.
Shaykh Ibn ‘Uthaymeen (may Allaah have mercy on him) was asked about this and he said:
The answer is that a contract of this type is not permissible, because it involves riba which is the price of the card, and it also means committing to pay interest if payment is delayed.