Parry spent most of last season on the New Orleans Saints practice squad, playing in one game.
The 6-3, 3-17-pounder was a fifth-round draft choice (151st overall) of the Indianapolis Colts out of Stanford in 2015, and started all 32 games for the Colts over the next two seasons.
Parry was released by the Colts during final roster cuts last year and joined the Saints practice squad on Sept. 4. He has 49 tackles, eight tackles for loss, four sacks and 11 quarterback pressures in his 33 career games.
The Vikings also released defensive tackle Dylan Bradley, who was signed as a free agent last year out of Southern Mississippi. Bradley played in four games and was in on two tackles, one a sack.