Spending four years at the University of Charleston in the NCAA, Draper had his first professional experience at Sydney Kings of Australia in the 2007-08 season, before signing for the French team Hyeres Toulon a season later. Signing for the Belgian side Oostende in December, Draper played for the 2009-10 season with Prima Veroli from the Italian second league. Taking the first significant steps of his career in the 2010-11 season, the prolific player was signed by the Croatian side Cedevita Zagreb in the 2010-11 season. After his successful performances within the two seasons there, he transferred to the Spanish side Real Madrid at the start of the 2012-13 season. Draper have been playing for Real Madrid for the last two seasons.

In the 2010-11 season, Draper was selected the MVP of Eurocup with Cedevita Zagreb, and was selected to the All-Eurocup team. Winning the Spanish League with Real Madrid in the 2012-13 season as well as the Spanish Cup in 2014, Draper also won the Croatian Cup in 2012 with Cedevita Zagreb. Having won the Spanish Super Cup in 2012 and 2013, Draper also plays for the Croatian National Team. The competent player played for the Croatian National Team in the 2011 and 2013 European Basketball Championship. Selected for the All-Team of the Southern Conference in the 2006-07 season as part of his college career, Draper was selected the best sixth man in the Australian League in 2008.
Playing in 20 matches in the Euroleague in the previous season, Draper had 1.7 points, 0.7 rebounds and 1.3 assists in 11.14 minutes per game.

He had 1.7 points, 0.9 rebounds and 1.7 assists in 12 minutes per game within 23 matches at the Spanish League.

Last year, in the Euroleague regular season fifth week match between Anadolu Efes and Real Madrid played in Madrid, Draper had 5 points, 1 assist and 1 steal. In the 10th week match played in Istanbul, he had 3 points, 1 assist and 1 steal.

Anadolu Efes signed a two-year deal with Dontaye Draper