Borković began karting in 1994 and became the Yugoslavian karting champion for six consecutive years from 1995 to 2000, establishing an early foundation of racecraft. After that sustained karting career, he made his circuit-racing debut in 2002 in the Serbian National-Class championship. He finished second in his debut season and went on to win the championship four consecutive times from 2005 to 2008.
After his run of success in the Serbian National-Class, Borković turned to hill climbing in 2010. Driving a Mitsubishi Lancer Evo 9, he won the Serbian Hill Climb Championship in his very first season, taking victory at all five events on the calendar. In 2011 he stepped up to the European Hill Climb Championship and finished second in his debut season. He won the European title outright in 2012, still at the wheel of the Mitsubishi Lancer Evo 9, completing a rapid progression from national to European champion in just two hill-climb seasons.
Borković transitioned to the European Touring Car Cup (ETCC) in 2013, driving initially in a SEAT León TFSI before switching to a Chevrolet Cruze LT for the final two meetings of the season. He finished third in the Super 2000 class with five podiums and one win. The 2015 season brought his greatest touring car achievement: entered with the NIS Petrol Racing Team in a SEAT León Cup Racer, he claimed the ETCC Single Make Trophy class championship.
On 20 November 2013 it was confirmed that Borković would compete in the World Touring Car Championship for 2014, joining Campos Racing in one of their TC1 RML Chevrolet Cruze entries. He delivered his first WTCC podium on 26 October 2014. For 2015 he moved to Proteam Racing, driving a Honda Civic WTCC, but contested only the opening round in Argentina before withdrawing from the series. Proteam Racing was unable to accommodate Borković's height in the cockpit, and there was further dissatisfaction with the car's specification.
Following his WTCC departure, Borković competed in TCR-category racing, eventually winning the TCR Eastern Europe championship in 2020. Alongside circuit competition he also pursued rally, winning the Serbia Rally Championship in 2019, 2020, and 2022 — a parallel career thread that underscored his broad competence across different formats of motorsport.
Borković served as a member of the National Assembly of Serbia from 2016 to 2020. He stood on the Serbian Progressive Party's electoral list — as an aligned independent rather than a party member — in the 2016 Serbian parliamentary election, in which the list won 131 of 250 parliamentary mandates. In the assembly, Borković was a deputy member of the committee on spatial planning, transport, infrastructure, and telecommunications, and of the committee on education, science, technological development, and the information society. He did not seek re-election in 2020.
Borković's career represents one of the widest-ranging records in Serbian motorsport. The combination of a European Hill Climb Championship, a European Touring Car Cup title, a TCR Eastern Europe championship, three national rally crowns, and WTCC appearances — all built from a foundation of six consecutive Yugoslavian karting titles — marks him as an athlete of unusual versatility. His parallel service as a legislator added a dimension rare among active racing drivers.