Yes, United States citizens can use their debit/credit card while travelling in Cuba.
99% plus of United States citizens traveling to Cuba know that dollars are the primary currency needed to navigate through the country. While getting businesses to accept dollars can be risky, if not tricky, the common practice is once you land at the airport you venture to the exchange office and convert your dollars into Cuban currency (currently the rate is 1:.87, so you quickly lose 13 cents but your options are limited if non-existent).
“We offer both a debit card attached to a checking account and a credit card that is usable in Cuba,” Officer, Centennial/Stonegate Bank
The one legitimate U.S. bank which provides a credit card to use in Cuba is a Mastercard issued by Centennial Bank formerly Stonegate Bank of Florida. The bank issues a credit card as well as debit card. They have offices in Arkansas, Alabama and New York. That is very important because to receive a debit card you must personally go to one of their offices. The reason is because the debit card is tied to a checking account. The credit card can be applied for online.
One other critical part of the application process is you must submit a supplemental certification that you are authorized to travel to Cuba. It is assumed if you have properly planned for your trip to Cuba you have the creditworthiness of obtaining the credit card or debit card.
Finally, as most already know the U.S./Cuba relationship is fluid and subject to change without notice, so the best advice is to ask questions and verify with legitimate sources so that you can enjoy your visit.