The Marlins designated Turner for assignment Tuesday, two days after the former first-round pick was roughed up in his most recent start.
Turner was just 4-7 with a 5.97 ERA while shifting between the rotation and the bullpen this season.
The 23-year-old had been considered one of Miami's top pitching prospects after being acquired by the Marlins as part of the July 2012 trade that sent established veterans Anibal Sanchez and Omar Infante to the Detroit Tigers. Turner has gone just 8-19 since the deal, however, and owns a 9-21 record with a 4.77 ERA over 53 major league appearances (45 starts).
To make room for Turner on the 40-man roster, the Cubs designated Ryan Kalish for assignment. Kalish hit just .242 with four RBI in 39 games with the Cubs this season.