The move comes two days after the Packers placed linebackers Jake Ryan and C.J. Johnson on injured reserve.
Crawford, who is listed at 6-foot-2 and 239 pounds, collected four sacks last season at the University of Illinois. He recorded 80 tackles, four forced fumbles and three fumble recoveries in 36 career games with the Illini.
Crawford served as a team captain as a senior and was named All-Big Ten honorable mention by the coaches.
Ryan, who sustained a torn ACL in practice was slated to start next to Blake Martinez at inside linebacker this season. Oren Burks and Ahmad Thomas were considered as possible replacements for Ryan, according to Packers defensive coordinator Mike Pettine.
The 26-year-old Ryan quickly clutched at his knee and screamed in pain last week as teammates gathered around him, per Michael Cohen of The Athletic.