He played junior hockey for the Prince George Cougars, Swift Current Broncos, and the Lethbridge Hurricanes of the Western Hockey League from 2001 to 2005. Redenbach led the league in scoring in 2003-04, winning the Bob Clarke Trophy.
The Phoenix Coyotes chose him 77th overall in the 2003 NHL Entry Draft but failed to sign him in the two-year deadline. Instead the Boston Bruins signed him as a free agent in 2005 and assigned him to the Providence Bruins. He played there until November, 2007, when he was traded to the Coyotes for Philippe Sauvé.
From 2005 to 2008 Redenbach had played with a number of minor pro teams without any NHL time. In 2008 he decided to give Europe a try. He played a season with the Odense Bulldogs in Denmark's AL-Bank Ligaen. In 2009 he moved to the SaiPa Lappeenranta of Finland's SM-Liiga.