Sofuoglu won Class B of the Turkish Supersport Championship in 2000 and claimed the German Yamaha R6 Cup in 2002. He then competed in the European Superstock Championship, finishing second and third over two seasons, before entering the Supersport World Championship full-time in 2006 following three races in 2003.
Sofuoglu dominated the 2007 Supersport World Championship season, winning five of the first eight races and breaking the record for the most wins in a single season. His victories that year included a two-lap charge from sixth to first at Monza, a win on his first visit to Donington Park in wet conditions, and further wins at Losail, Spain, and Assen. He clinched the title with three races remaining, becoming Turkey's first major motorsport world champion. He signed with Ten Kate Honda for the following three seasons.
In 2008 Sofuoglu moved into the Superbike World Championship riding a Ten Kate Honda CBR1000RR but had limited success and returned to Supersport with the team for 2009. He then reclaimed the Supersport title in 2010, finishing on the podium in every race of the season in a three-way championship battle that also included Eugene Laverty and Joan Lascorz.
Racing for Kawasaki in 2012, Sofuoglu claimed his third Supersport World Championship at the Portuguese Grand Prix, with one race remaining. He added two more titles in 2015 and 2016 with Kawasaki Puccetti Racing, cementing his position as the dominant figure in the class across more than a decade of competition.
Sofuoglu made his Moto2 debut at the end of the 2010 season with the Technomag-CIP team, stepping in as a replacement for Shoya Tomizawa following Tomizawa's fatal accident at Misano. Qualifying was rained out, placing him on the front row, and he led for much of the race on his first ever dry laps on the machine before finishing fifth. He remained with the team through the 2011 season, his best result being a second place at Assen.
A crash during training in early February 2017 broke a finger bone requiring two operations. Later that season, on 30 September 2017, Sofuoglu broke his pelvis in three places during the Superpole session at a championship round in France. He was flown to Istanbul by air ambulance, and after a recovery period of only five weeks returned to contest the final round at Qatar, finishing third. In 2018, following further injury at Phillip Island, he announced his retirement from racing ahead of the Imola round. He made a brief comeback appearance at Imola, qualifying third, but withdrew from the race after the sighting lap.
Sofuoglu was elected to the Turkish Grand National Assembly in June 2018 as a Justice and Development Party representative for Sakarya Province. He has stated that he donates his parliamentary salary to charity.
Sofuoglu speaks German, French, English, and Turkish. His race number 54 is derived from the license plate code of his home province of Sakarya. His father, Irfan Basri Sofuoglu, is a motorcycle repairman. Two of Sofuoglu's brothers, both local motorcycle racers, died in accidents: his eldest brother Bahattin in a road traffic accident in 2002, and his brother Sinan during a race training incident at the Izmit Korfez Circuit in May 2008. Sofuoglu married Julia Looman in September 2014.