Rodney has made 46 relief appearances this season, recording 25 saves and a 3.09 ERA over 43.2 innings. The 41-year-old is the latest piece acquired to bolster Oakland's bullpen, as the Athletics have also added Jeurys Familia from the New York Mets and Shawn Kelley from the Washington Nationals in recent weeks.
Chalmers, meanwhile, has tossed just five innings with Single-A Beloit this season. The 21-year-old was selected by the Athletics in the third round of the 2015 draft.
Entering Thursday's schedule, the Athletics held a three-game lead on the second wild-card spot in the American League, and trailed the West-leading Houston Astros by five games.