Born in Smederevska Palanka, Ćirković represented FC Admira Wacker Mödling, SC Perchtoldsdorf and ASV Vösendorf as a youth.

Ćirković scored his first senior goal on 7 June 2019, netting the opener in a 1–1 away draw against SK Rapid Wien II.

On 2 February 2021, after featuring rarely in the main squad, Ćirković was loaned to Serbian SuperLiga side FK Mačva Šabac for the remainder of the season.

[2] He scored his first professional goal on 7 March, netting his team's third in a 3–1 home win over FK Proleter Novi Sad, but was unable to avoid the club's relegation.

On 20 July 2021, Ćirković moved to Spain and signed a three-year contract with Primera División RFEF side Gimnàstic de Tarragona.