Born in Kraljevo, Drašković started playing football in the local academy Bubamara, after which moved to youth categories of Čukarički.
[1] Finally he joined BASK, making a single appearance in the 2009–10 Serbian League Belgrade campaign.
[2] Next he moved to the Dunav Zone League side Zvižd, where he stayed between 2010 and 2011.
[4] At the beginning of 2016, Drašković moved to Šumadija 1903, where he spent the rest of the 2015–15 season in the Serbian League West.
[5] In summer 2016, Drašković moved to the Maltese side Victoria Wanderers, where he affirmed as a goal poacher in the 2016–17 Maltese FA Trophy, scoring a twice in the third round 5–0 victory over Mġarr United.