In return, Oakland sent Single-A pitcher Dakota Chalmers to Minnesota.
Rodney is 3-2 with a 3.09 ERA in 46 appearances this season. The 41-year-old has 25 saves, with 50 strikeouts and 19 walks in 43⅔ innings. Rodney has 325 career saves, 17th in baseball history.
The Athletics are 68-47 this season and entered Thursday night with a three-game lead for the second American League wild-card spot.
Chalmers, a 21-year-old right-hander, was a third-round pick in the 2015 draft. He has made two appearances this season for Single-A Beloit. He is 7-7 with a 4.08 ERA in four minor league seasons with Oakland.
Information from The Associated Press was used in this report.