The Mets selected Orze's contract from Triple-A Syracuse on Saturday.
Orze has spent all season at Triple-A, logging a 3.76 ERA and 1.33 WHIP over 38.1 innings. The 26-year-old right-hander will now join the Mets as replacement bullpen depth for Ty Adcock and will be making his MLB debut whenever he gets into a game.