Twardzik started off his career with Sachsen Leipzig before being signed by Hertha Berlin. On 1 February 2009, he was signed by Celtic, a week before his 16th birthday. Patrik suspended his education when he moved to Celtic. His mother also moved to Scotland to help him adjust to his new life.
In September 2012, Twardzik signed a contract extension with the club, which kept him until 2014. After a year, Twardzik joined Scottish Championship side Livingston on loan that will kept him until January. Twardzik made his debut for the club on 23 November 2013, where he set up a goal, in a 5–1 victory over Greenock Morton.[