Yekta began his career at İzmirspor playing for the club four years, before signing for Kasımpaşa in 2007, where he was handed the number 5 kit. He made his professional debut on 25 November 2007 in a 2–0 loss over Rizespor coming in as substitute in the 55th minute. He finished his first season for the club with 16 attempts and one assist.
His performances with Kasımpaşa led to interest from several league clubs. On 11 January 2011, Yekta passed his medical and signed for four years with Galatasaray. He made his first appearance for the club one week later against Sivasspor in a 1-0 home win. He also made his first 2013-14 UEFA Champions League appearance on 26 February 2014 against Chelsea, coming in as a substitute in a 1-1 home draw.