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 43 2/3 innings.
The Athletics are 68-47 this season and entered Thursday night with a three-game lead for the second AL 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.