On June 22, 2017, Čančar was selected with the 49th overall pick in the 2017 NBA draft by the Denver Nuggets. On June 13, 2018, Čančar signed a two-year deal with Spanish club San Pablo Burgos.
On August 1, 2019, Čančar signed his rookie contract with the Denver Nuggets.
On Jan 15, 2020, against Charlotte Hornets Čančar scored his first FG in regular NBA season.
On April 16, 2015, Čančar signed a five-year contract with Union Olimpija.
On June 30, 2016, he left Olimpija and signed with Serbian team Mega Leks.
Čančar has been a member of the Slovenia national basketball team. He played with the team at EuroBasket 2017, where he won the gold medal with his country.