Oklahoma QB Baker Mayfield -- who got DESTROYED by cops when he drunkenly tried to run from police -- will not have to go to jail.

As we previously reported, the 2016 Heisman trophy finalist was arrested in Arkansas in Feb. after cops tried to confront him about an alleged violent altercation earlier in the evening ... but the QB went nuts and tried to flee the scene. He was form tackled by a cop who shoulda been a linebacker.

Officials tell TMZ Sports Mayfield cut a plea deal with prosecutors last week in which he pled guilty to public intoxication, disorderly conduct and fleeing ... and in exchange, they dropped the resisting arrest charge (the most serious charge).