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. In 2000 he moved to Amica Wronki.
Before 2004-2005 season he joined Wisła KrakóWest
Zieńczuk was elected the best Ekstraklasa player in the 2007-2008 season by "Sport" magazine. Also, he was named to the Ekstraklasa Best XI in the 2007-2008 season by other players in Polish Football players" Association voting.
In the summer 2009, he joined Greek club Skoda Xanthi. After one season, he returned to his home country and joined Lechia Gdańsk.
After a half season spell, he moved to Ruch Chorzów on one and a half year contract.
Zieńczuk played nine times for the Poland national football team Amica Wronki Wisła Krakow Individual.