DiNucci, 24, originally began his college career at Pittsburgh before transferring to James Madison for the 2018 season. The Cowboys used the No. 231 overall pick in the seventh round on him in 2020.
DiNucci signed a four-year, $3,390,148 rookie contract that includes a $95,148 signing bonus. He was waived on Tuesday.
In 2020, DiNucci appeared in three games for the Cowboys and completed 23-43 pass attempts for 219 yards. He also rushed six times for 22 yards.