The Bears were in need of depth in their backfield after Armando Allen suffered a hamstring injury in practice on Sunday. Allen is listed as week to week.
Brinkley appeared in 10 games last year for the San Diego Chargers. He's carried the ball 71 times for 227 yards and one touchdown in five NFL seasons.
The Bears host the Chargers in their second preseason game on Thursday.
To make room for Brinkley on the roster, the Bears waived wide receiver Marcus Rucker.