Peralta signed with the Seattle Mariners as an international free agent in April 2013. He made his professional debut that year with the Dominican Summer League Mariners and spent the whole season there, going 3-3 with a 1.46 ERA in 13 games (ten starts). In 2014, he pitched for the Arizona League Mariners where he pitched to a 1-6 record and 5.29 ERA in 12 starts, and in 2015, he returned there, going 2-3 with a 4.11 ERA in 11 games (nine starts).
On December 9, 2015 the Mariners traded Peralta, Daniel Missaki and Carlos Herrera to the Milwaukee Brewers for Adam Lind.   He spent 2016 with the Wisconsin Timber Rattlers and the Biloxi Shuckers, pitching to a combined 4-4 record and 3.62 ERA in 82 innings pitched.
Peralta pitched 2017 with the Carolina Mudcats and Biloxi.   In 25 games (19 starts) between the two clubs he was 3-8 with a 2.63 ERA and 1.16 WHIP.  The Brewers added him to their 40-man roster after the season.  MLB.com ranked Peralta as Milwaukee's tenth ranked prospect going into the 2018 season. 
Peralta began 2018 with the Colorado Springs Sky Sox and was called up to Milwaukee on May 13 to make his MLB debut. He debuted that same night against the Colorado Rockies at Coors Field. He recorded 13 strikeouts and gave up zero runs in 5.2 innings, setting the Brewers franchise record for strikeouts by a first time starter.