The team announced the move on Tuesday.
Lawrence played for the Hamilton Tiger-Cats last season in the CFL, his second in the league.
The 25-year-old spent his past two amateur seasons at Minnesota, a junior-college signing under then-coach Tim Brewster. Lawrence has been in NFL training camps before, but he has never appeared in a game. He has also played in the United Football League.
AP NFL website: www.pro32.ap.org