The Colts signed Rainey, a former fifth-round draft pick, on Wednesday.
The Pittsburgh Steelers released Rainey during the offseason after he was accused of slapping his girlfriend.
Rainey also was ticketed for driving with a suspended license and given a citation for "defiant trespass" at a racetrack casino last year, according to the Pittsburgh Post-Gazette.
Rainey rushed for 102 yards and two touchdowns on 26 carries as a rookie with Pittsburgh.
Kickoff return is where Rainey could be most valuable for the Colts (7-3). David Reed, the team's current returner, has made bad decisions with his returns, often leaving the Colts with poor field position.
Rainey has returned 39 kicks for 1,035 yards, an average of 26.5 yards per return.