Teams that lose “more or better” free agents than they acquired the previous year are eligible for compensatory picks.
The seventh-round pick is for safety Cody Davis, who signed a two-year contract with the Jacksonville Jaguars that included $2.5 million in guarantees.
The Rams, defeated by the New England Patriots in the Super Bowl, have seven picks in the draft, which will be held April 25-27 in Nashville.
The picks are at No. 31 in the first round, 94 (third round), 99 (third-round compensation), 133 (fourth), 169 (fifth), 203 (sixth) and 251 (seventh).
The NFL scouting combine begins next week in Indianapolis.