Alex Georgescu has identified the following sources:

Sevda Ayluçtarhan's thesis on Abdullah Cevdet's translations (Boğaziçi University, 2007) mentions:
  • Hasan Bedreddin and Mehmed Rıfat's Othello (1876) based on the French version by Ducis (which lacks the Duke's couplet). 
  • Mihran Boyacıyan apparently finished translating Othello in 1896 but wasn’t allowed to publish until 1912 (due to censorship). This version - title: İngiltere meşâhîr üdebâsından Şeykspîrin eser-i kıymetdârı Otello - is WorldCat OCLC 643752383 (copy in BSB, Munich)
Versions are on sale at www.nadirkitap.com (July 2011) by:
  • Orhan Burian (tr. Othello 1943; and see his article ‘Shakespeare in Turkey’ in Shakespeare Quarterly 2 2, Apr. 1951)
  • Turan Oflazoğlu and A. Vahit Turan
  • Özdemir Nutku
  • Fatma Çolak
  • Dr Refet (1931) (according to Turkish Wikipedia, this was also a translation via the French)
A search on WorldCat also identified:
  • Yusuf Mardin (1945: OCLC 56015744)