Jerry Crasnick of ESPN first reported that Miller was traded to the Orioles.
Miller is 3-5 with a 2.34 ERA, 13 holds and a 0.90 WHIP this season. Rodriguez is 3-7, with a 4.79 ERA in 16 starts.
The Orioles are 60-49, and lead the American League East by 2.5 games, entering Thursday.
Miller, who has a career 5.06 ERA, started his career with the Tigers in 2006, and was dealt to the Marlins in 2008 as part of the trade that brought two-time American League Most Valuable Player Miguel Cabrera to Detroit.
- Sarah Barshop and Scooby Axson