Kumanovo born Ćirić started his career at Sloga Jugomagnat. Via Metalurg Skopje he moved to Pelister. From the Bulgarian side CSKA Sofia he signed for FK Vardar again and went to FC Aarau. German Bundesliga side 1. FC Nuremberg bought him in 1997 for a fee of 1 million Swiss Franks.
In 2003 Ćirić joined the Club once again and retied in 2006 at Offenbacher Kickers.
Subsequently he became chairman of Macedonian second tier team FK Merida.