Ascanio was signed as an undrafted free agent in 2001 by Atlanta. He began his professional career with the GCL Braves, where he went 4–1 with a 1.37 ERA and 17 strikeouts at age 18. The next year, with the Rome Braves, he went 3–3, with a 3.84 ERA and 64 strikeouts, as well as a career-high 9 saves, in 34 games.
On July 13, 2007, Ascanio was called up by the Braves after Wilfredo Ledezma had trouble getting back to the U.S. after going home to Venezuela during the All-Star break. Ascanio made his debut the same day, pitching the ninth inning of a 9–1 win. Ascanio allowed one run on three hits in his first Major League appearance, striking out two in the process. He was sent down on July 31 and called up again on August 24. He earned his first Major League win on September 14 pitching the last two innings of a 13-inning game. He finished the season 1–1 with a 5.06 ERA.
On May 10, 2009, Ascanio was called up by the Cubs from Triple-A Iowa after possessing a 1.01 ERA in 262⁄3 innings pitched as a starter. He was expected to start in the back of the bullpen. He appeared in 14 games for the Cubs, with a 3.52 ERA.