He was placed on the Atlanta Braves 40-man roster for the first time in 2009 when he made three appearances for the major league team, and later on April 16, 2011, to replace the disabled Peter Moylan.[2] His Major League debut was on July 12, 2009, against the Colorado Rockies. On April 28, 2011, Asencio was optioned back to the Triple-A Gwinnett Braves.[3]
For the entire 2010 Atlanta Braves season, Asencio was on the team's restricted list because of visa problems. It was discovered later in the year that Asencio had used a false name, Luis Valdez, and birthdate.[4][5]
Cleveland Indians
On March 29, 2012, Asencio was traded to the Cleveland Indians for cash considerations.[6] Asencio was designated for assignment on May 28, 2012.[7]
Chicago Cubs
The Chicago Cubs claimed Asencio off waivers on June 1, 2012.[8]
Milwaukee Brewers
Asencio signed a Minor League contract with an invitation to Spring training with the Milwaukee Brewers on Nov. 5, 2012.[9]
Baltimore Orioles
On March 25, 2013, he was traded to the Baltimore Orioles for a player to be named later or cash. He started the 2013 season with the Triple-A Norfolk Tides. He was recalled by the Orioles on July 12,[10] and pitched one inning of relief against the Toronto Blue Jays that night. He was designated for assignment on July 28, 2013.[11] He elected free agency on October 4, 2013.[12]
On January 22, 2015, he signed a minor league contract with the Chicago White Sox.[15] He was released on May 29.[16]
Leones de Yucatán
On April 18, 2017, Asencio signed with the Leones de Yucatán of the Mexican Baseball League. He was released on June 6, 2017. In 25 games of relief 26 innings he went 2-1 with a 2.42 era and 28 strikeouts.
Saraperos de Saltillo
On May 23, 2019, Asencio signed with the Saraperos de Saltillo of the Mexican League. He was released on June 4, 2019. In 5 games of relief 4 innings he went 0-1 with a 4.50 era and 2 strikeouts