Career
Vršajević"s first professional club was NK TOŠK Tešanj. Here he spent the 2003-2004 season before moving to Željezničar. He spent only one season at Željezničar before Čelik Zenica acquired his services.
He remained at Čelik for two seasons, often in and out of the first team
From Čelik, Avdija moved to Czechoslovakian side Air Corps Sparta Prague but never made an appearance for them, spending loan spells initially at Saskatchewan Kladno and then at 1. Football Club Tatran Prešov. Tatran made his loan move permanent in 2009 and he spent the following two seasons there, making 60 appearances and scoring three goals.
He was played as either a right back or a right winger at Tatran. Avdija moved back to Čelik in 2011, spending one season at the club where he made a further 21 appearances.
As he only signed a one-year contract at Čelik and chose not to renew it when the season ended, Avdija moved to Croatian side Hajduk Split, signing a three-year contract.
He made his debut for Hajduk on the 22nd of July, 2012 in a 0–0 draw against Istra. Immediately becoming the club"s first choice right back, Avdija made 30 appearances in all competitions in his first season at Hajduk. In the 2013-2014 season, manager Igor Tudor changed his role in the team often.
Throughout the season he found himself at left back, right back and right wing, once again making 30 appearances in all competitions.
In June 2015, Vršajević left Hajduk Split, after agreeing mutual termination with the club On July 18, he signed with newly promoted Turkish side Osmanlıspor.
In 2006, Vršajević was called to Bosnia and Herzegovina under-21 side by then coach Ibrahim Zukanović. Vršajević was named in the Bosnia and Herzegovina 23-man squad for their first World Cup participation ever in the 2014 World Cup.
On 25 June 2014, he scored his first goal and Bosnia"s third in the 83rd minute to make it 3–1 for Bosnia against Iran in the last group match, where he also made his World Cup debut.