The signing of Rush reunites him with former Cowboys head coach Jason Garrett, who was hired this off-season as the Giants' offensive coordinator. Rush and Garrett spent the past three seasons together in Dallas.
Rush, 26, has appeared in five career NFL games, completing only one pass for two yards. The Cowboys signed the Central Michigan product as an undrafted free agent in 2017.
Rush joins a quarterback room that includes starter Daniel Jones, the No. 6 overall pick in the 2019 draft, and veterans Alex Tanney and Colt McCoy. Undrafted rookie Case Cookus, who signed with the Giants this off-season as a free agent, gives the team five quarterbacks on the roster.