The White Sox designated Turley for assignment Tuesday.
Turley was claimed off waivers by the White Sox on Sunday.
Turley was traded from the Pirates to the Athletics on Thursday in exchange for cash considerations, Martin Gallegos of MLB.com reports.
Turley was designated for assignment by the Pirates on Tuesday.
Turley (0-3) allowed three runs on two hits and hit a batter in one inning in a loss to Cleveland on Sunday.
Turley (0-1) gave up a run on a hit and a walk in two-thirds of an inning, taking the loss Monday versus the Brewers.
Turley did not allow a baserunner and struck out one across a scoreless inning to earn the save in the second game of the Pirates' doubleheader Thursday against the Cardinals.
The Pirates selected Turley's contract Thursday.
Turley was added to the Pirates' 60-man player pool.
Turley (elbow) was shipped to Triple-A Indianapolis on Thursday, John Dreker of PiratesProspects.com reports.