The White Sox outrighted Peralta to Triple-A Charlotte on Thursday.
The White Sox claimed Peralta off waivers from Seattle on Sunday before designating him for assignment two days later, but he will officially remain in the organization after clearing waivers. The 26-year-old southpaw posted a 4.05 ERA in 20 innings with the White Sox last season, though he owns a 9.24 ERA through 12.2 Triple-A frames this year.