Huston started his film career with a small screen adaptation of Spartacus, where he played Flavius. He then went on to having more prominent roles in such films as Factory Girl, playing the American poet Gerard Malanga, the horror film Shrooms, Outlander and Shrink.
In 2010, he played the minor role of Royce King in The Twilight Saga: Eclipse. He appeared in HBO's Boardwalk Empire as Richard Harrow, a severely disfigured World War I marksman turned gangster. On 16 December 2010, it was announced Huston would be made a series regular after appearing in five episodes of the first season.
After this he went on to be directed by Al Pacino in the 2011 film Wilde Salomé and to having starring roles in Not Fade Away, Two Jacks and Night Train to Lisbon. In 2012, he played the part of narrator on avant-garde musician John Zorn's album A Vision in Blakelight, an homage to William Blake.
In 2013, he appeared in David O. Russell's comedy-drama American Hustle, as Pete Musane. Later that year, Huston played Charles Bruno in Strangers on a Train at London's Gielgud Theatre. In 2015 he appeared as Ira Levinson in Nicholas Sparks' The Longest Ride. In 2019 Huston played Bobby Kennedy in the Martin Scorsese film The Irishman.
In 2020, he had a supporting role in the fourth season of the FX black comedy crime drama Fargo as Odis Weff, a corrupt Kansas City police detective with severe OCD.
In 2023, Huston made his directorial debut with Day of the Fight, starring Michael Pitt as a once renowned boxer whose since fallen on hard times. The film had its premiere out of competition in the Orizzonti Extra section of the 80th Venice International Film Festival.