Rodriguez has appeared in 25 games for the Brewers this season and has a 1-1 record with a 1.09 ERA and 10 saves. In his 11-year career, he has a 2.64 ERA with 304 saves.
Delmonico, 20, was a sixth-round pick in 2011 and is hitting .244 in High-A Frederick this season.
The Brewers are currently 19 games behind the St. Louis Cardinals in the National League Central and have very little chance of making the postseason. The Orioles are only 2.5 games behind the Boston Red Sox in the American League East. The trade will hopefully boost the Orioles pitching staff, which came into Tuesday's action 13th in ERA in the 15-team AL.