Pestano has spent time with Cleveland and Triple-A Columbus this season. He went 0-1 with a 5.00 ERA in 13 games with the Indians, making his last major league appearance on July 10 against the New York Yankees.
The Indians received minor league right-hander Michael Clevinger in Thursday's deal. The 23-year-old Clevinger is 4-3 with a 4.31 ERA in 18 starts at two Class-A stops this season. He was selected by Los Angeles in the fourth round of the 2011 draft.
The 29-year-old Pestano made his major league debut with Cleveland in 2010 and is 5-8 with 11 saves and a 2.93 ERA in 192 career games.