Swarzak, a right-hander, was the Twins' second-round pick (61st overall) in the 2004 June draft out of Nova High School in Davie, Florida. As a sophomore, Swarzak pitched to a 11–1 record with a 1.16 ERA and 120 strikeouts and was named to the All-County team and second team All-State. In 2003, he finished 14–1 with 142 strikeouts. In his senior season, in which he went 14–2, with 147 strikeouts, Swarzak was named to the 2004 All-County and Class 5A All-State teams. He had a scholarship to pitch for the Louisiana State University Tigers, but instead chose to sign with the Twins on June 22, 2004, for a $575,000 bonus.
Swarzak was #15 on the Baseball America Top Gulf Coast League Prospects list in 2004. He was Midwest League Pitcher of the Week (from May 16–22, 2005), the Twins' Pitcher of the Month (May 2005), Midwest League All-Star, and #8 on the Baseball America Top Midwest League Prospects list in 2005. In 2006, he was Florida State League Pitcher of the Week (from August 7–14, 2006) and a FSL Post-Season All-Star.
Swarzak was one of the top rated prospects in the Twins' farm system before a fifty-game suspension for violation of Minor League drug policy on April 20, 2007 sidetracked his career. He tested positive for marijuana. After having started the season with the Double A New Britain Rock Cats, upon his reinstatement from the restricted list on June 11, he was reassigned to the Class A Advanced Fort Myers Miracle. After three games with Fort Myers, he returned to New Britain.
He began the 2008 season with the Rock Cats, and went 3–8 with a 5.67 earned run average. After a promotion to Triple-A, his record actually improved to 5–0 with a 1.80 ERA in seven starts. He was added to the Twins' 40 man roster, and spent his first spring with the Twins in 2009. Following Spring training, he was reassigned to Rochester. Swarzak suffered from a lack of run support in Rochester to start the season. Despite an ERA of 1.59 in his first three starts, his record stood at 0–3.
His record improved to 3–4 with a 2.25 ERA when he got the call to the majors on May 20. He filled in the starting rotation for the injured left-handed starter Glen Perkins.
Swarzak made his major league debut for the Twins on May 23, 2009 in a home game against the Milwaukee Brewers. He pitched seven shutout innings, giving up five hits and two walks while striking out three. The Twins won the game 6–2, earning Swarzak his first major league win.
After a line drive broke his foot, Swarzak's 2010 season was statistically awful as he spent the whole year in the minors. His ERA finished at 6.21 in AAA Rochester.
Swarzak rebounded in 2011, contributing both in long relief and in spot starts for the Twins. He pitched a total of 102 innings, going 4–7 in 27 games.
In 2012, Swarzak started five games for the Twins while making 39 appearances out of the bullpen, pitching to a collective 96 innings of work. Swarzak began 2013 on the disabled list with fractured left ribs he suffered while "wrestling around a little bit." He was activated on April 7 and used primarily as a long reliever for the rest of the season. In 48 games, he went 3–2 with a 2.91 ERA, striking out 69 in 96 innings.
On November 25, 2014 the Twins announced that Swarzak had been outrighted off the 40-man roster and elected free agency. He joined the Cleveland Indians on a minor league contract for the 2015 season, but was released in May and signed with the Doosan Bears of the Korea Baseball Organization.
Swarzak signed a minor league contract with the New York Yankees on February 5, 2016. He began the 2016 season with the Triple-A Scranton/Wilkes-Barre RailRiders, and was promoted to the major leagues on June 7. At the end of the season, Swarzak elected free agency over an assignment to Scranton/Wilkes-Barre.
On January 23, 2017, Swarzak signed a minor league contract with the Chicago White Sox.
On July 25, 2017, Swarzak was traded by the Chicago White Sox to the Milwaukee Brewers for outfielder Ryan Cordell.