Wieland was drafted by the Texas Rangers in the fourth round of the 2008 Major League Baseball Draft. He signed with the Rangers and did not play for San Diego State. Wieland spent 2009 with the Class AHickory Crawdads where he posted a 5.31 ERA in 19 games. He opened 2010 with the Crawdads, but an improved 3.34 ERA in 15 games earned him a promotion to the California League High-A Bakersfield Blaze in July. In 2011, Wieland started the year with the Myrtle Beach Pelicans, the Rangers' new High-A affiliate, and then graduated to Double-A in late June. On July 29, 2011, while pitching for the Frisco RoughRiders, Wieland threw a no-hitter against the San Antonio Missions, the Padres Double-A affiliate. Wieland had a 1.23 ERA in 7 starts for the RoughRiders.
San Diego Padres
On July 31, 2011, Wieland and Robbie Erlin were traded to the San Diego Padres for Mike Adams. He finished the year with the Double-A Missions, posting a 2.77 ERA in 5 starts. He had 8.7 strike-outs per 9 innings across all three clubs in 2011. Wieland started 2012 with the Triple-ATucson Padres, but only made 2 starts before he was called up to the Major League team. Wieland was called up to join the Padres' rotation when both Tim Stauffer and Dustin Moseley went on the disabled list early in the season. He made his Major League debut on April 14, 2012, against the Los Angeles Dodgers, allowing six runs in five innings to take the loss. Wieland made five starts for the Padres, losing four of them, and posted a 4.55 ERA before he went to the disabled list in May with shoulder tightness. He underwent a season-ending Tommy John surgery on July 27, 2012. Wieland began the 2013 season on the 60-day disabled list as he was still recovering from the surgery. He began a throwing program at around mid-season but he suffered a number of setbacks due to soreness and a stress reaction and missed the entire season. He underwent arthroscopic surgery on his elbow at the start of the 2014 season and did not make his return to the Padres until September 6, 2014. In four appearances for the Padres in 2014, he allowed nine runs in 11 innings. He finally picked up his first MLB win on September 24 against the Colorado Rockies.
Los Angeles Dodgers
On December 18, 2014, he was traded to the Los Angeles Dodgers in exchange for Matt Kemp, Tim Federowicz and cash. He was assigned to the AAA Oklahoma City Dodgers. Wieland was called up to the Dodgers on May 6, 2015, to start a game against the Milwaukee Brewers. He allowed six runs in 4 innings and was promptly optioned back to AAA following the game. He made a second start on September 9, allowing two runs in four innings. In 21 starts for Oklahoma City, he was 10–5 with a 4.59 ERA. The Dodgers re-signed him to a one-year, $590,000 contract after the season to avoid salary arbitration.
Seattle Mariners
On January 12, 2016, Wieland was traded to the Seattle Mariners in exchange for minor league infielder Erick Mejia. The Mariners traded Wieland to the Atlanta Braves on September 14, and he was assigned to Triple A Gwinnett.
Yokohama DeNA BayStars
On 7 November 2016, it was announced that Wieland had signed with the Yokohama DeNA BayStars in the NPB for the 2017 season.
Kia Tigers
On December 5, 2018, Wieland signed with the Kia Tigers of the KBO League. He became a free agent following the season.
