If the car has the luck to find a rock of more or less his mass, taking the mass and speed into account, can it make a considerable amount of damage in an asteroid?
The answer to this depends on dozens of variables, such as angles, speeds, and asteroid compositions. We would also have to define "a considerable amount of damage."
However, videos of a comparable sized rock plowing into the moon on Mar 17, 2013 show just how powerful such an impact can be. The video claims that particular impact was equivalent to 5kT of TNT.
I would not want to be either party in such an impact.