The move comes after the Rams waived receiver Pharoh Cooper, who last season made the Pro Bowl as a kick returner.
Anderson is expected to provide needed depth at running back through the final two regular-season games and the playoffs.
Gurley's most trusted backup, Malcolm Brown, was placed on injured reserve after he suffered a clavicle injury in Week 13.
Against the Eagles, the Rams relied on second-year pro Justin Davis and rookie John Kelly to back up Gurley. But Davis suffered a shoulder injury and is listed as day-to-day, and Kelly -- a sixth-round pick who was inactive through 12 games -- appeared overwhelmed when inserted.
The Panthers released Anderson on Nov. 12. He joined the Oakland Raiders for a week before he was released.
A former Pro Bowl selection, Anderson has rushed for 3,155 yards and 20 touchdowns in his six-year career.
Cooper, whom the Rams selected in the fourth round of the 2016 draft from South Carolina, was placed on injured reserve after he underwent ankle surgery following a Week 1 victory over the Raiders.
Cooper, who has never had a significant presence in the Rams' passing game, averaged a league-best 27.4 yards on kick returns last season but just 21.3 yards on 13 kickoffs this season.