Parsons was signed by the Atlanta Braves as an undrafted free agent in 2013 out of Jackson State Community College. The Braves sent him directly to low-A Rome in the South Atlantic League, a fairly aggressive initial assignment for a 20 year-old straight out of community college, but Parsons performed well, posting a 2.63 ERA over 109 2/3 innings with a 1.02 WHIP and a 21/101 BB/K ratio.
Parsons struggled when he was promoted to high-A Lynchburg in the Carolina League in 2014. He made 23 starts, throwing 113 innings, posting a 5.02 ERA and 1.35 WHIP along with a 34/96 BB/K ratio.