Burns was drafted by the Cleveland Indians in the eighth round of the 2009 Major League Baseball draft out of the University of Arizona.[1]
He was traded to the San Diego Padres on December 16, 2011, for Aaron Cunningham.[2]
The Padres called Burns up to the majors for the first time on August 3, 2012,[3] and sent him down to the Tucson Padres on August 5. He was recalled on August 11 when Huston Street was placed on the disabled list.[4]
Burns was acquired by the Texas Rangers on November 28, 2012, and split the 2013 season between the Rangers and the Triple-A Round Rock Express.[5] Wilfredo Boscán was sent to the Padres on December 6 to complete the trade.[6]
Burns was claimed off waivers by the Tampa Bay Rays on June 30, 2014, and optioned to the Double-A Montgomery Biscuits.[7] He also played for the Triple-A Durham Bulls in 2014.
Burns was claimed off waivers by the Toronto Blue Jays on September 28, 2014.[8] He was designated for assignment on January 14, 2015,[9] and outrighted to the Triple-A Buffalo Bisons on January 16. He was assigned to the Double-A New Hampshire Fisher Cats on April 2. Burns elected free agency on November 6, 2015.[10]
On March 15, 2016, Burns signed with the Lancaster Barnstormers of the Atlantic League of Professional Baseball.
On December 15, 2016, Burns signed a minor league contract with the New York Mets organization.[11] He split the 2017 season between the Double–A Binghamton Rumble Ponies and Triple–A Las Vegas 51s. In 46 combined appearances, he logged a 4.70 ERA with 63 strikeouts and 19 saves in 53+2⁄3 innings pitched. Burns elected free agency following the season on November 6.[12]