Sure, the burning part isn't the problem.

Diesel has small amounts of lubricants, and those are very much needed for all the tiny little moving parts in fuel injectors and probably even in the engine itself. RP-1 doesn't have those.

Also, I know jet fuel will absolutely destroy just about every rubber not specifically designed for it, and that may apply to RP-1 as well.

Also, starting your rocket fuel car in winter is probably going to be a real chore, since the vaporization point is much higher, and modern cars don't come with preheaters that can handle that anymore (thanks to those fuel injectors).