This is Pangea Software's Cro-Mag Rally updated to run on modern systems.

In Cro-Mag Rally you are a speed-hungry caveman named Brog who races through
the Stone, Bronze, and Iron Ages in primitive vehicles such as the Geode
Cruiser, Bone Buggy, Logmobile, Trojan Horse, and many others.  Brog has at
his disposal an arsenal of primitive weaponry ranging from Bone Bombs to
Chinese Bottle Rockets and Heat Seeking Homing Pigeons.

In addition to single-player racing where one player races against the
computer, there are also several different multi-player modes including Tag,
Capture the Flag, and Survival. Up to four players can play on a single
computer in split-screen mode.