After spending his development years in Partizan's youth academy, Drinčić made his senior debuts with the club's affiliated side Teleoptik.

In the next two years, Drinčić was sent on loan to Spartak Subotica and Budućnost Banatski Dvor, enjoying a successful stint with the latter, scoring nine league goals from 28 appearances in the 2005–06 season.

[2] He however broke his shinbone in a friendly just two weeks after joining the club, causing him to make a half-year break from competitive football.

[3] After recovering, Drinčić was never able to break into the starting eleven and appeared in just four league games for the club, eventually leaving at the end of the season.

On 3 November 2010, Drinčić made his UEFA Champions League debut in a 1–4 away loss to Chelsea at Stamford Bridge, coming off the bench in 67th minute as substitute for Aleksandr Sheshukov.

On 18 October 2014, Drinčić scored again against Red Star and again from a free kick, helping club to reach a 1–0 victory in 147th Derby.

[16] In June 2015, Drinčić signed a two-year contract with Israeli club Maccabi Haifa with an option for another season.

[27] He made his debut for the Montenegro national team in the country's inaugural match versus Sweden in September 2007.