To make room for Hinshaw on the 40-man roster, right-handed pitcher Arodys Vizcaino has been transferred to the 60-day disabled list.
Hinshaw, 29, has gone 1-1 with a 4.50 ERA in 31 relief appearances this season, making his first Major League appearance since 2009 on May 9.
He struck out 36 batters and walked 20 in 28 innings before being designated for assignment Aug. 14.
Vizcaino, 21, had Tommy John surgery during Spring Training, causing him to miss the entire 2012 season. He is expected to be back to action for Spring Training '13.
Mark Clements is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.