Shields, 30, visited with both the Rams and Cleveland Browns as he tries to resume his career.
While with the Green Bay Packers in 2016, he suffered a concussion in the first game and was sidelined for the rest of the season. He was released by the Packers in February 2017, but no team signed him.
Shields was a starter for the Packers in 2013, 2014 and 2015, and he was selected to the Pro Bowl in 2014. He has 18 interceptions in his six NFL seasons, not counting 2016.
It remains to be seen whether he can claim much playing time with the Rams, who acquired cornerback Marcus Peters recently. However, cornerbacks Trumaine Johnson and Nickell Robey-Coleman could become free agents next week.