Rimkevičius played for FK Tauras Tauragė, FBK Kaunas, FK Liepājas Metalurgs, FK Silute, FK Šiauliai, FK Bekentas, Atlantis FC. and Asteras Tripoli F.C.. He made his international debut against Latvia in June 2010, scoring three times for his country in seven caps, one against Estonia and two against Armenia.