The 5-foot-11, 195-pound cornerback has played 16 NFL games and started since signing with Jacksonville as an undrafted free agent in April 2010. Gordon spent most of that season on the Packers practice squad and played in two games late in Green Bay's Super Bowl-winning season.
He joined the Rams last season, first on the practice squad before playing in 14 games.
The Central Michigan alum was an all-Mid-American Conference selection in 2009.
Indy has been trying to fill a hole at the second cornerback spot since training camp began. Cornerback Jerraud Powers and veteran safeties Antoine Bethea and Tom Zbikowski are all expected to start for the Colts.