The Game Proposes to Baby Mama ... ON TAPE

The Game just popped the question to his baby mama ... after dating her for 7 years -- and we caught the entire ringtastic moment on tape.

Game dropped to one knee moments ago at the L.A. elementary school where his girlfriend Tiffney teaches -- and we won't ruin it ... BUT SHE SAYS YES.

Game and Tiffney have two kids together -- a son named King Justice and a daughter named Cali. Game also has a third child from a previous relationship.