Gorgodze played for the Georgia national rugby union team in 71 matches, including 13 as a captain.

His first club was Lelo in the Georgian Top League, he was soon selected for the Georgia national team and made his debut in 2003 against Spain, at the age of just 18 and not long after he started playing rugby.

Gorgodze started his career at Montpellier mainly as a reserve in the side and didn't get much game time.

After the 2007 Rugby World Cup, Gorgodze started playing for Montpellier a lot more regularly and was their first choice lock.

In November 2013, as his contract with Montpellier was expiring, he signed a three-year deal with Toulon to take effect with the 2014–15 season.

[8] His competitive debut with Toulon was delayed due to a knee injury during a preseason friendly with Racing Métro; and missed the start of the 2014–15 season.