Kaya scored his first goal for the club against Samsunspor on 7 January 2012 in the 51st minute of a 2–0 comeback, with the game ending 4–2 for Galatasaray. In the 2011–12 season, he played 30 games and was a key member of the championship-winning squad. He continued to be first choice centre-back for the club and country, delivering calm and confident performances despite against top teams such as Manchester United and, internationally, against the Netherlands. He finished his second year with 36 appearances in all competitions. On 18 November 2013, his contract was extended for three years until 2016.
Kaya has played for all levels of the Turkish national team, including the under-21 level despite being at a younger age at the time. He made his debut for senior Turkish side on 29 February 2012, playing the entire game against Slovakia in a 2–1 loss. He is part of the Turkish national team for Euro 2016.