The Marlins traded Acton to the Twins on Thursday in exchange for minor-league pitcher Logan Whitaker.
The 27-year-old righty was DFA'd by the Marlins on Sunday to make room on the 40-man roster for Leo Jimenez. Acton has pitched 2.1 scoreless innings in Triple-A to begin the season, and moving into a Twins organization that doesn't have much bullpen depth should help his chances of returning to the big leagues at some point.