"We've been talking about bringing in some good energy guys that are going to work hard and compete hard physically and he's going to do that for us," Canucks general manager Jim Benning said Friday.
The pick, No. 85, was acquired by Vancouver earlier Friday as part of the multiplayer trade that sent center Ryan Kesler to the Anaheim Ducks.
Dorsett, 27, scored four goals and finished with eight points and 128 penalty minutes in 51 regular-season games for the Rangers. He had one assist and 19 penalty minutes in 23 Stanley Cup Playoff games.
A seventh-round pick (No. 189) in the 2006 NHL Draft by the Columbus Blue Jackets, Dorsett has 31 goals, 73 points and 855 penalty minutes in 331 games with the Blue Jackets and Rangers.