Asencio amassed a 4-0 record and a 2.15 ERA with 41 strikeouts in 37 2/3 innings with the Norfolk Tides.
He managed to notch 20 saves, the top mark in the International League.
In 39 career MLB appearances with the Atlanta Braves, Cleveland Indians and Chicago Cubs, Asencio has managed a 5.23 ERA.
The O’s acquired the 30-year-old from the Milwaukee Brewers in March for a player to be named or cash.
Jurrjens pitched in two games for Baltimore this season, allowing four earned runs in 7 1/3 innings.
In 16 starts for Norfolk, he has notched a 6-6 record and a 4.18 ERA.