Zieńczuk began his career at hometown club Lechia Gdańsk. Subsequently he joined Polonia Gdańsk, but quickly returned to Lechia where he made his senior debut.[2] In 2000, he moved to Amica Wronki. Before 2004–05 season he joined Wisła Kraków. He won the Ekstraklasa championship three times with Wisła Kraków. Zieńczuk was elected the best Ekstraklasa player in the 2007–08 season by "Sport" magazine.[3] Also, he was named to the Ekstraklasa Best XI in the 2007–08 season by other players in Polish Footballers' Association voting.[4]
In the summer 2009, he joined Greek club Skoda Xanthi. After one season, he returned to his home country and joined Lechia Gdańsk.[5][6] After a half season spell, he moved to Ruch Chorzów on a one-and-a-half-year contract.[7]