Jenkins, 27, has been a starter for all four seasons of his NFL career with the Rams.
This past season, he had three interceptions, a forced fumble and 65 tackles. The 2012 second-round pick has 10 career interceptions, including three returned for touchdowns in his rookie season.
The Rams’ talented secondary takes a hit with the loss, but it would have been tough for the team to retain both of its free-agent corners. Los Angeles chose to use its franchise tag on fellow corner Trumaine Johnson.