Barraclough played college baseball at St. Mary's College of California. He was drafted by the Minnesota Twins in the 40th round of the 2011 Major League Baseball Draft, but did not sign. He was then drafted by the St. Louis Cardinals in the seventh round of the 2012 MLB Draft. was traded to the Miami Marlins for Steve Cishek on July 24, 2015.
Barraclough was called up to the majors for the first time on August 7, 2015.