Sure. In my area, it just has to have headlights, brake lights, turn signals, horn, DOT tires, exhaust, some sort of title or certificate of origin, proof of insurance, etc.
I've seen converted Sprint Cars into street legal cars around here, so yes, you can convert a race car to a street legal ride... although it may not be real comfortable.
Check out this NCTS truck that was on the Power Tour. It was really cool.