As a redshirt freshman in 2013, Rodrigues completed 3 of 6 passes for 67 yards with a touchdown and an interception. He shared the backup job with Jeff Lockie during the season, but neither emerged as a clear-cut No. 2 during spring practice.
Rodrigues decided to leave after meeting with coach Mark Helfrich on Monday morning, according to a Comcast SportsNet Northwest report.
"Football wasn't working out here, and that is why I am leaving," Rodrigues told CSNNW. "I am not leaving because of how people treated me or how much it rains here. I am leaving simply based on this football decision."
It was not immediately clear where Rodrigues, ESPN.com's No. 12-ranked quarterback in the Class of 2012, intends to transfer.
Lockie completed 8 of 13 passes for 57 yards without a touchdown and one interception in 2013. He leads a group of three quarterbacks remaining behind Mariota, a Heisman Trophy front-runner, on the roster along with Damion Hobbs and walk-on Taylor Alie, both of whom redshirted last season. The Ducks also signed Morgan Mahalak, ESPN.com's No. 9-ranked dual-threat quarterback, to their most recent recruiting class.