In 2004 Jaba Kankava started his football career with Dinamo Tbilisi, where Gia Geguchadze was just appointed as head coach. Geguchadze started to create a new club with youngsters and Kankava became a main member of them. In his first year, Kankava won the Georgian Cup, and played in the UEFA Europa League scoring the winning goal against Slavia Prague and contributing to the qualification for the group stages.

After one season at Dinamo, Kankava moved to Alania Vladikavkaz, where he played 12 matches, before signing a contract with Arsenal Kyiv in 2005. At Arsenal Kyiv, he played 24 matches and scored 4 goals.

Kankava played 5 games in 2006 FIFA World Cup qualifying and 9 games in UEFA Euro 2008 qualifying. He also played 2 friendlies i 4 in 2006, 2 in 2007 and 2 in 2008.

In 2007, Kankava agreed to sign a three-year contract with league rival Dnipro. Newly arrived Kankava was among the starting squad from the first games but received a red card against Dynamo Kyiv because of a tough tackle and missed several games and was among the bench players. In eight years at Dnipro, he played 91 matches and scored 4 goals.

On 30 March 2014, Kankava saved the life of FC Dynamo Kyiv captain, Oleh Husyev, after Husyev was briefly knocked unconscious in a collision and swallowed his tongue which blocked his airway. Kankava reacted immediately by sticking his fingers in Husyev’s mouth to dislodge his tongue and clear his airway. On 12 April 2014 before Dnipro played Metalurh Zaporizhya at the Dnipro Arena, Kankava was awarded the Order of Merit for his actions in Dnipropetrovsk.

In 2015, Kankava joined Ligue 1 club Reims. In July 2017, he agreed to the termination of his contract which ran until 2018.

On 22 November 2018, Kankava signed a new two-year contract with FC Tobol.