Career
OFK Beograd
Born in Sombor, Dražić spent his formative years with FK Teleoptik and FK Partizan. He subsequently went on trial at Russian club Football Club Rubin Kazan, before returning to Serbia and signing his first professional contract with OFK Beograd at the age of 18. Dražić made his official debut for the club on 21 September 2013, coming on as a second-half substitute for Aleksandar Čavrić in a 0–2 away loss to his former side Partizan.
He scored his first professional goal on 19 October, netting his team"s first in a 2–3 home loss against FK Radnički 1923.
He finished his first senior season with four league goals from 23 appearances. Celta
On 7 August 2015, Dražić signed a five-year deal with Spanish Louisiana Liga side Celta de Vigo.
He made his first appearance as a substitute, coming on for Theo Bongonda in a 1–1 draw against South Dakota Eibar. Dražić represented Serbia at the 2014 Union of European Football Associations Under-19 Championship, making three appearances.