The 30-year-old Camden, N.J., native was signed by the Padres as an amateur free agent in 2006 and made his Major League debut with San Diego on May 16, 2009.
That year, his only season in the big leagues, he appeared in 48 games out of the bullpen, posting a 3-3 record and 4.14 ERA in 45 2/3 innings of work. He struck out 33 batters and walked 23 in that span.
Burke signed with the Orioles as a free agent on Feb. 10, 2012, but he never reached the big leagues and was granted free agency on Saturday.
He spent the 2012 season between Double-A Bowie and Triple-A Norfolk in the Orioles' system, combining to go 3-1 with a 1.53 ERA in 44 games out of the bullpen.