"I pay by credit card."
Translation:Πληρώνω με πιστωτική κάρτα.
The article can be ommited because you're talking about sth general (not a specific kind of credit card) and it's implied that it is supposed to be only one.
You could say Πληρώνω με την πιστωτική κάρτα, without ommiting the την, but that would make it just a bit more specific, wouldn't it? I hope I helped. ^.^