Indiana also sent a 2014 second-round draft pick to Philadelphia, which accumulated five second-round picks before Thursday's trade deadline.
Turner, 25, gives the Pacers a talented, young wing player whom they can keep beyond this playoff run.
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Turner has averaged 17.4 points, six rebounds and 3.7 assists for the Sixers this season. He was the No. 2 overall pick in the 2010 NBA draft.
Turner will be a restricted free agent this summer.
Granger, 30, has averaged 17.6 points in his career for the Pacers, but only 8.3 points this season while coming off the bench. He spent the early part of the season recovering from a calf injury.
He also played in only five games last season because of a knee injury.
The Pacers were expected to lose Granger as a free agent this summer.