Vrapi began his career while still a teenager, playing for KF Partizani Tiranë. Regarded as one of the best young Albanian talents at the time, he was also captain of the Albania national under-19 football team. He worked his way up through the ranks at KF Partizani Tiranë and joined the first team during the 2001-2002 season, though he did not feature in any league game that season. This prompted Vrapi to sign with KS Lushnja, a weaker team in the Albanian Superliga, to gain some experience.
At KS Lushnja he quickly established himself in the first team. He played seventy-six games and scored four goals for the club between 2002 and 2005. His impressive displays prompted one of the best teams in the country, KS Elbasani, to sign the left back in 2005. His most successful season came at KS Elbasani during his first spell there in the 2005-2006 season. He played thirty-four games and scored two goals that season and was one reason KS Elbasani won the Albanian championship. After his triumph with KS Elbasani, in 2006 Vrapi moved to KS Teuta Durrës, where he almost repeated his success with KS Elbasani, when Teuta Durrës finished second behind KF Tirana in the Albanian Superliga. During the 2006-2007 season he played twenty-nine games and scored two goals. After spending only one season in Durres, Vrapi changed teams again, moving back to KF Tirana. This turned out to be a mistake. KF Tirana struggled all season, finishing a disappointing sixth place in the Albanian Superliga, the team's lowest league position in years. During that poor season Vrapi played twenty-seven games without scoring a goal. The Albanian international defender decided to go back and play where he had spent the best years of his career, KS Elbasani. He was greeted by his former team with open arms as they had paid a fee believed to be in the region of $140,000 for re-signing the left back.