He played in Major League Baseball (MLB) for the Toronto Blue Jays and the Seattle Mariners.

In his first season at UCLA, Rasmussen made only 10 appearances and 2 starts after sustaining a broken left foot off a line drive comebacker in the third inning of his 2008 collegiate debut against UC Santa Barbara.

[5][6][7] During the 2009 season, Rasmussen made 18 appearances, posted a record of 4-2 with a 6.75 ERA, while totaling 51 strikeouts and 26 walks in 442⁄3 innings.

On March 6, he earned a win against Nebraska in the finale of a 3-game series, recording 10 strikeouts in five innings as the Bruins starter, limiting the Huskers to one unearned run and three hits.

According to the Under Armour 2010 Draft Scouting Report: "Rasmussen is a pretty advanced college lefty with an interesting combination of pitchability and stuff.

He's a bit undersized, which might concern some, but he does a nice job mixing his pitches and keeping hitters guessing.

He was selected to the Southern League All-Star team but was unable to play because he was promoted to the Triple-A Albuquerque Isotopes.

He was called up for his first trip to the major leagues on May 20[17] and made his debut that night, getting David Ortiz to groundout in a 7–4 win.

[18] Rasmussen recorded his first major league strikeout on May 26, against Logan Forsythe of the Tampa Bay Rays.

[22] On July 31, 2015, Rasmussen was traded with Nick Wells and Jake Brentz to the Seattle Mariners for Mark Lowe.