The Angels also designated left-hander Bobby La Fromboise for assignment Monday.
Torreyes made his major league debut last season in eight games with the Los Angeles Dodgers, going 2 for 6.
The 23-year-old Venezuelan prospect is a six-year minor league veteran, but the Angels are his fifth organization since May. The Dodgers traded him to the Yankees earlier this month, but New York designated him for assignment.
Torreyes could provide depth at second base, where Johnny Giavotella is expected to be the Angels' starter again after a solid 2015.
The Angels also have Cliff Pennington, Taylor Featherston, Rey Navarro and Gregorio Petit in contention for an infield spot when spring training opens next month.