The move continues a trade deadline haul for the Blue Jackets, who are going all-in after acquiring forwards Matt Duchene and Ryan Dzingel from the Senators as well as backup goalie Keith Kinkaid from the New Jersey Devils.
By trading away the picks for McQuaid, the Blue Jackets have only two draft picks in 2019: a third-rounder and a seventh-rounder.
The Rangers, meanwhile, are stockpiling draft picks; they have 10 in 2019, including five in the first two rounds.
McQuaid, 32, spent nine years with the Boston Bruins before heading to the Rangers this season. He is averaging 17:28 minutes per game and has two goals and three assists in 36 games.