Rogers played in the team's preseason opener last season but was placed on injured reserve on Aug. 31 with a blood clot in his leg.
The Giants can use the 6-foot-4, 350-pound Rogers after releasing Canty on Wednesday. The team cut Canty, linebacker Michael Boley and running back Ahmad Bradshaw this week in an effort to create salary-cap space and move in a different direction after missing the playoffs last season.
Canty started alongside Linval Joseph at defensive tackle. Rogers now will be in the mix to fill Canty's spot along with Marvin Austin and Markus Kuhn. Rocky Bernard, who was a valuable reserve this past season, is a free agent.
Rogers, a 13-year veteran, has started 128 of his 156 games with Detroit, Cleveland and New Orleans. He has 602 tackles and 37.5 sacks in his career.