Career
Barisic began his career in 2002 with the ACTAS before moving to Canberra Deakin in July 2003. In January 2004 he signed his first professional contract with Melbourne Knights, then left in the summer of 2006 for Europe and signed a contract for Germany-based Oberliga Nord club, Arminia Hannover. Melbourne Knights
On 13 December 2007 he signed with his former club Melbourne Knights in the Victorian Premier League.
Gold Coast United
On 10 December 2008 he was signed by Gold Coast United on a one-year contract.
At Gold Coast United he made six appearances and scored one goal in his first season there. He was signed on for one further year.
In his second season at GCU, he made 11 appearances and again scored one goal. Persebaya1927
After leaving Gold Coast, "Bara" signed for Indonesian side Persebaya Surabaya in the Indonesian Premier League.
He did very well there, scoring 11 in 14 games.
Arema Malang
He then signed for another Indonesia Super League side, this time Arema Cronus F.C., where he managed 8 goals in 15 appearances. East Bengal
Andrew officially signed for East Bengal on the 10th of January 2013. On 3 April 2013, he scored brace in 2013 AFC Cup against Singaporean opponent Tampines Rovers in group stage match.
Return to Melbourne Knights
Barisic returned for the 4th time to Melbourne Knights in January 2015 scoring 12 goals in 16 games.
South China
On 31 December 2013, Barisic signed for South China. At South China, Barisic managed 13 goals in 18 appearances, 6 in the Hong Kong PL, 2 in AFC Qualification and 1 in the Senior Challenge Shield.
Kerala Blasters Football Club
Barisic then signed for newly formed Kerala Blasters Football Club in the newly formed Indian Super League. In the ISL side, Barisic managed 11 appearances in which Kerala came 2nd.
Eastern Football Club
On the 1st of July 2015 Andrew Signed with Hong Kong Premier League Side Eastern Football Club.