Rinne made his professional debut for Örebro SK in the first round of the Allsvenskan on 30 March 2014, coming on as a half-time substitute for Oscar Jansson and keeping a clean sheet while playing in Örebro's 2−1 come from behind victory over Halmstads BK. Rinne once again came off the bench on 8 May, replacing the injured Jansson and preserving the clean sheet in a 0−0 draw with Falkenbergs FF. His first start for the club came three days later, conceding two goals as Örebro fell to IFK Göteborg 2−1. Rinne played in the second round of the Svenska Cupen on 20 August 2014, keeping a clean sheet as Örebro defeated Eskilstuna City FK 2−0.