Rodney, 42, has seen his ERA balloon to a career-worst 9.42 this season. He had returned to Oakland for 2019 after the A's exercised a $5.25 million club option.
Rodney has pitched for 10 teams in a 17-year career and ranks 18th in MLB history with 325 saves.
The A's called up left-hander Wei-Chung Wang from Triple-A Las Vegas. He has 22 games of major league experience, all with the Milwaukee Brewers.