Parsons was recalled from Triple-A Gwinnett on Tuesday.
Parsons will join the big club ahead of the second half of Tuesday's twin bill to offer additional bullpen help after Atlanta's bullpen was tasked with six innings of work in Game 1. The 25-year-old has yet to make an appearance at the major-league level this season, though he owns a solid 3.03 ERA across 65.1 innings with Gwinnett.