The Rams have not waived Havrisik, and coach Sean McVay said they do not anticipate making that move.
Havrisik signed with the Rams in Week 8 to replace Brett Maher, who was released in October.
Crosby brings experience, success and "crunch-time moments," McVay said to a team making a late-season playoff push.
Crosby played his first 16 NFL seasons with the Green Bay Packers but did not re-sign with the team during the offseason. The veteran kicker went 24-for-25 from inside 50 yards last season but was 1-for-4 from kicks longer than 50 yards.