The Collaborative International Dictionary of English v.0.48:

Squarer \Squar"er\ (skw[^a]r"[~e]r), n.
   1. One who, or that which, squares.
      [1913 Webster]

   2. One who squares, or quarrels; a hot-headed, contentious
      fellow. [Obs.] --Shak.
      [1913 Webster]