Anderson left the White Sox on Monday in Cleveland and returned to Chicago to join his wife, Bria, in welcoming their second child, a daughter named Paxton. He was placed on the paternity list Wednesday ahead of the team's 8-3 win against the Indians.
The 23-year-old Hamilton opened the regular season on the injured list due to right shoulder inflammation. He posted a 1.74 ERA over 51 2/3 innings of work split between Double-A Birmingham and Triple-A Charlotte in 2018.
In a corresponding roster move, the White Sox optioned right-handed pitcher Dylan Covey to Triple-A Charlotte. He had allowed two earned runs in 1 1/3 innings across two appearances this season.