Anderson will hold a showcase for teams Jan. 23, Bob Nightengale of USA Today reports.
The Royals released Anderson on Thursday, Anne Rogers of MLB.com reports.
The Royals designated Anderson for assignment Saturday.
Anderson (1-1) allowed a hit and struck out one without walking a batter over a scoreless inning, earning the win in Game 1 of Wednesday's doubleheader versus the White Sox.
Anderson (0-1) allowed two runs on two hits without walking or striking out a batter over one-third of an inning to take the loss Monday versus the Orioles.
Anderson has allowed two runs on three hits and a walk with two strikeouts over three Cactus League innings.
The Royals and Anderson avoided arbitration by agreeing to a one-year, $1.575 million contract Thursday, Bob Nightengale of USA Today reports.
Atlanta traded Anderson to the Royals on Friday in exchange for cash, Joel Sherman of the New York Post reports.
Anderson (shoulder) will begin a rehab assignment Tuesday with Triple-A Gwinnett, Justin Toscano of The Atlanta Journal-Constitution reports.
Anderson (shoulder) has begun throwing off a mound, Justin Toscano of The Atlanta Journal-Constitution reports.