If you have any issue with a cab and you want to use a CC to go to DC from VA or from DC to VA or within VA, simply call Red Top - 703-522-3333. They will meet at the passenger pickup line (where regular vehicles pick you up, and not at the taxi stand).
All the cabs take credit cards and they have passenger card swipe devices right by your seat. Very few DC cabs take CCs, although this number has increased owing to the decision a few years ago do dispense with the "zone" system and actually charge a metered rate.
BTW, in my discussions with RedTop drivers, the management charges them 6% on a credit sale...So, make it worth their while....