Bicaj started his career in with his home town club, Dinamo Tirana at a very young age.

[4] On 6 June 2017, Bicaj joined fellow Albanian Superliga side Flamurtari Vlorë by signing a contract until 2017–18 season.

[5] He scored his first goal for the team on 22 October in the matchday 7 of Albanian Superliga, a late header against Kamza at home which brought Flamurtari to winning ways after three consecutive draws.

[10] On 30 July 2018, Teuta Durrës announced to have signed Bicaj on a one-year contract, reuniting him with his former teammate Bledi Shkëmbi, now as team manager.

[11] He made his senior debut on 2 June 2010 in Albania's 1–0 win over Andorra at Qemal Stafa Stadium, where Bicaj entered as a substitute in the last moments.