Kaya joined Galatasaray's youth academy from Altay's youth team when he was 15. On 25 February 2007, when he was playing against older young players in the season of Süper Gençler Ligi against Beşiktaş, in the fifth minute of the game, a kick from Batuhan Karadeniz collided with his head, forcing him to leave the game; he later went to a hospital to undergo head surgery. The start of the 2008–09 season saw foreign interest in Kaya rise, with reports that Italian club Internazionale were monitoring him ahead of a transfer deal, though the rumours never materialized. Kaya's first Süper Lig appearance was against İstanbul B.B. on 19 February 2009. After not receiving significant playing time, he joined fellow Süper Lig club Gaziantepsporon loan in January 2010 for the remainder of the season, and, in the summer of 2010 he signed for Turkish First League side Kartalspor on loan. On 18 October 2010, he scored two goals in the A2 Lig game against Altay.
Return to Galatasaray
At the beginning of the 2011–12 season, Kaya was not typically selected for Galatasaray's starting line-up, but following injuries to other players, notably Gökhan Zan, and a fall in form of Servet Çetin, Galatasaray coach Fatih Terim granted him a chance to prove himself. Following a series of solid performances, he soon became first-choice centreback alongside the Czech Tomáš Ujfaluši. Kaya scored his first goal for the club against Samsunspor on 7 January2012 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 November2013, his contract was extended for three years until 2016.
International career
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.
Personal life
Kaya's grandfather was Torbesh and he emigrated from Macedonia to the Turkish city ofİzmir. He is the youngest of three brothers.