Born to a German father and a Serbian mother,[2] Rensing joined Bayern in 2000 from TuS Lingen,[3] and went on to develop his talent in the club's youth sides.

Rensing made his Bundesliga debut on 21 February 2004, playing the entire 90 minutes of the 1–0 home win against Hamburger SV.

[9] On 15 April 2006, Rensing was involved in a strange incident prior to a match against Arminia Bielefeld.

He took a warm-up shot that struck goalkeeper Oliver Kahn blackening his eye and forcing him to sit out the game.

[14] Following Kahn's retirement in 2008, Rensing was given a chance as Bayern's first-choice goalkeeper, but was unable to cement his spot.

[15] Following a poor start to the 2009–10 season, his experienced teammate Hans-Jörg Butt replaced him as the Bavarian club's first-choice goalkeeper.

In November 2010, Rensing joined Leicester City on trial[18] but rejected the subsequent contract offer.

[26] Rensing continued being the first choice keeper during the 2015–16 season[27] with the exception of the first round cup match against Rot Weiss Essen where Lars Unnerstall played.

[31] Having been Germany's number one goalkeeper at the U-19 level, Rensing joined the hosts' squad at the 2004 UEFA European Under-21 Championship finals, although he did not get off the bench.