Do American airlines planes have car charger plugs?

Yes, but it depends on what kind of plane you're on. AA has several types of planes in their fleet. Some use the car cigarette lighter style of outlet, and others use normal outlets like you have at home. In either case, not all seats on the plane have them. Call AA (1-800-433-7300) and they can assist with trying to seat you near an outlet, or answering whether one is already in the seat you have reserved. Or go to aa.com > Travel Information > During Your Flight > Onboard Technology > Power Ports.