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Ramirez, 27, was designated for assignment by the Giants at the end of April.
He has 18 strikeouts and four walks so far this season.
Ramirez divided his 2016 season between the Chicago Cubs, the Milwaukee Brewers and the Minnesota Twins. In his two previous seasons with the Cubs he posted 3.21 and 1.44 ERAs, through 19 and 50 games respectively.
Toronto already has nine relievers on its active roster.
Blue Jays’ Devon Travis hoping slow start is behind him