Sikora was born in Chicago, Illinois, and lived in the Jefferson Park and Norwood Park neighborhoods. He attended Notre Dame College Prep for high school. He studied acting at Chicago Columbia College, where he received a BA in theater.
As a child, Sikora appeared in a McDonald's commercial with Michael Jordan. He made his Broadway debut in 2006 after he was cast as one of the leads on The Caine Mutiny Court-Martial. He is also an ensemble member of Chicago's Shattered Globe Theatre Company.
Sikora made his acting debut in an episode of The New Adam-12 after playing extras on a few TV shows. He was cast as Johnny in Rudy. After making small appearances in TV shows and films such as Early Edition, Turks, The Watcher, and Ghost World, he was cast in two episodes of Third Watch.
In 2003, Sikora was cast as Roger in the direct-to-video biographical-drama film Gacy. After making a few appearances on low-budget movies, he was cast in the Golden Globe-nominated Normal, which he feels was his "break-through" moment when the star of the movie, Tom Wilkinson, told him that "all you have to do is think the line and the camera will read it".
He also took part in plays and was part of the Geffen Theatre's production of Fat Pig and the Lost Angeles Theatre's production of Killer Joe. He made a lot of TV appearances between 2005–2012, appearing in major network shows including ER, Grey's Anatomy, Criminal Minds, Without a Trace, CSI: Miami, Prison Break, Lost, and Dollhouse. He was later cast in the 2007 horror film Night Skies.
He was later cast in two episodes of Law & Order: Special Victims Unit in 2010. That same year, he was cast as an Orderly at the Mental Hospital in Shutter Island. In 2011, he was cast in the television pilot for Body of Proof, as well as being signed in a full role in Adult Swim's comedy horror TV series The Heart, She Holler, playing the Sheriff. In early 2012, he signed on to appear in Safe as the son of the head of the Russian mafia. He returned to theater in September 2012 with The Freedom of the City.
In October 2013, he was cast in Starz! original drama series Power.
In 2012, he appeared in Jack Reacher, in which he played a sniper wrongfully accused of gunning down random people in Pittsburgh and Jack Reacher is called in to prove that he is innocent.