Drmic attended the Australian Institute of Sport and was recruited to the United States to play at Boise State with teammate Igor Hadziomerovic. As a freshman in 2011–12, Drmic started all 29 games for the Broncos, averaging 12 points per game and set a school record for three-pointers by a freshman (57). At the end of the year, he was named honourable mention All-Mountain West Conference (MWC).
As a sophomore in 2012–13, Drmic raised his scoring to 17.7 points per game, leading the Broncos to the 2013 NCAA Tournament in the process. As a junior in 2013–14, he was named second-team All-MWC for the second year in a row, as well as All-District by the United States Basketball Writers Association.
Prior to the start of his senior season, Drmic was named first-team preseason All-MWC. However, he managed just seven games in 2014–15 after sustaining an ankle injury that ruled him out for the rest of the season. He subsequently applied for a medical hardship to play in 2015–16 as a fifth-year senior.
In 2015–16, Drmic appeared in 31 games with 25 starts, averaging 13.4 points, 4.4 rebounds and 1.4 assists per game. He subsequently earned All-Mountain West Honorable Mention selection by the media. Drmic finished his college career as the school's all-time three-point record holder, the school's games record holder, two points shy of the school's all-time leading scorer, and at No. 5 on the Mountain West Conference all-time scoring list.
On 5 May 2016, Drmic signed a two-year deal with the Adelaide 36ers of the National Basketball League. Drmic appeared in 27 games for the 36ers during the 2016–17 regular season and played an important role off the bench, averaging 14 minutes per game. He averaged 5.7 points and 3.4 rebounds per game, connecting on 45.2 percent of his field goal attempts. He led all rookies in scoring and rebounding, and as a result, he was named the recipient of the NBL Rookie of the Year Award. He became the fourth 36ers player to win the award, joining Mike McKay (1985), Chris Blakemore (1993) and Aaron Bruce (2009).
In March 2017, Drmic joined the Southern Tigers of the Premier League.
Drmic competed for Australia at the 2011 FIBA Under-19 World Championship, where he averaged 15.4 points per game in the nine matches and helped the Emus to a sixth-place finish.
Drmic's older brother, Frank, played in the NBL with the South East Melbourne Magic, Victoria Titans, Sydney Kings and South Dragons between 1996 and 2007, winning a championship with the Magic in 1996.