Born in Edmonton, London, of Turkish Cypriot descent, Rıza started his career as a youth with English club Arsenal and made his first team debut on 2 November 1998 against Derby County in the League Cup. During the 1998–99 season, he went on loan to ADO Den Haag for three months.
In the 1999–2000 season, he moved to West Ham United, but again was unable to break into the first team. He went on loan to Barnet and Cambridge United, and signed a permanent deal with the latter in 2002. During the 2002–03 season he scored 17 goals for United, which prompted a move to Süper Lig side Denizlispor during the 2003 close season. In January 2006, he signed for Trabzonspor.
In February 2009 Rıza returned to English football with a trial at League Two club Shrewsbury Town, and impressed manager Paul Simpson. Rıza made his debut for Shrewsbury Town as a second half substitute against Rotherham United on 18 April 2009.
On 22 January 2010, he left Shrewsbury Town after struggling to break into the first team during the first half of the season, with Riza and the club coming to an agreement regarding paying off the rest of his contract. On 25 February he joined Aldershot Town until the end of the season.
Following the appointment of David Livermore as manager at Histon, Riza joined Histon on a non-contract basis and made his debut against Kettering Town in a Conference National fixture on 28 August. He scored his first goal for Histon when he scored a penalty in their league match against Hayes & Yeading United, which turned out to be the winning goal.
Everyone at Boreham Wood welcomes Omer to the Club and hope his stay with us is a long and successful one.