The Mets claimed Tonkin off waivers from the Twins on Wednesday, Abbey Mastracco of the New York Daily News reports.
Tonkin doesn't have any minor-league options remaining, so he'll be added to the Mets' 26-man active roster and will presumably join the big club for the start of its series three-game series in Los Angeles versus the Dodgers this weekend. New York designated lefty Tyler Jay for assignment to clear room on the 40-man roster for Tonkin, who has allowed four earned runs on eight hits and three walks over six innings across his four relief appearances this season between the Twins and an earlier stint with the Mets.