No, there is not a McDonald's credit card. McDonald's has never offered its own credit card, but McDonald's locations will accept credit cards from Visa, Mastercard, American Express, and Discover as valid forms of payment. In addition, McDonald's customers can pay with cash, debit cards, and digital wallets such as Apple Pay and Google Pay. McDonald's sells gift cards, called Arch Cards, too.
The closest McDonald's has come to offering credit cards is when they gave out a McGold card to the winner of a Monopoly promotion. The McGold card isn't a credit card, as it extends no line of credit. Instead, it offers cardholders free McDonald's food for a certain period of time. Naturally, this isn't a card that you can apply for, and very few people actually have it.
If you want a credit card that gets good rewards at McDonald's, check out 2022's best cards for restaurants and food delivery.