The Cowboys could clearly use some more quarterback depth with Andy Dalton in the concussion protocol.
Rush, 26, went undrafted out of Central Michigan back in 2017. He later signed a three-year, $1.66 million contract with the Cowboys and managed to make the 53-man roster all three seasons.
Rush signed his $2.1 million restricted free agent offer after being tendered by the Cowboys this offseason. He was later waived and claimed by the Giants before agreeing to a restructured deal.
New York added Rush to their practice squad before releasing him a few weeks ago.
For his career, Rush has appeared in five games for the Cowboys, completing one of three pass attempts for two yards. He has also rushed for 13 yards.