Terms weren't immediately available. Rogers, 33, played last season with the New Orleans Saints and had 22 tackles in 16 games.
Canty underwent knee surgery after the Super Bowl but is expected to be ready for the season opener, according to coach Tom Coughlin.
"Hopefully, I can bring some of my experience over the past few years and just fit in and play a part," Rogers said in a team news release. "I still most definitely feel that I can bring something to the table. I might not be exactly like I was in '06, but I still have some tricks and I still have some good push in me."
Rogers has made a total of 75 tackles in the past three seasons after having 76 tackles in 2008 with the Cleveland Browns. He had a career-high seven sacks in 2007 with the Lions.
Marvin Austin, the Giants' 2011 second-round pick, missed all of his rookie season with a pectoral injury he suffered in the preseason. Austin is expected to be ready for training camp, but general manager Jerry Reese said recently he was concerned about Austin since the defensive tackle has not played football for two years after missing the 2010 season at North Carolina because of an NCAA suspension.