If you want to ask in Spanish if you can ask your credit card you must say:

Puedo pagar con tarjeta de credito?

-Puedo: (verb) to can
-pagar: (verb) to pay
-con: (prep.) with
-tarjeta de credito: credit card

If what you want is to pay with cash you should say:

Puedo pagar con dinero (suelto) o con tarjeta?