While many RV parks and private, state and private campgrounds accept credit and debit cards for payment, many federal campgrounds can only take cash or check for first-come-first-served campsites. National Parks and some of the larger federal Recreation Areas may be able to provide this service because of the volume of customers coming through their gates and the convenience of electricity and an internet connection.
However, many of the US Forest Service campgrounds are in remote locations where electricity and internet service is not available. I guess you could say it's the price we pay for nature immersion. Brainard Lake Recreation Area (BLRA) in the Arapaho-Roosevelt National Forest near Boulder, CO, has experimented with satellite internet but the signal was not strong and consistent enough to be worthwhile. It was more frustrating for the customer than convenient.
You can pay for a campsite through the reservation system www.recreation.gov when you reserve at least 4 days in advance. However, extra vehicles and firewood must still be paid for at the campground. So, to save time and frustration, you might want to hit the ATM before arriving at the campground. We also take a personal check.
Out of the approximately 400 campgrounds we manage for the US Forest Service, PG&E and California State Parks, here is a list of the few that take plastic for payment:
California: Brannan Island
Florida: Alexander Springs and Salt Springs
Utah, Pineview Reservoir: Anderson Cove, Cemetery Point and Port Marina
Utah, Flaming Gorge: Lucerne
Virginia: Bolar Mountain