The Verdict: Need More Info
You will be able to apply once you have been married for three years, provided you are still married and living together then.
Article 16 of the Turkish Citizenship Law (Law 5901) lets a foreigner who has been married to a Turkish citizen for at least three years, and is still married, apply for citizenship. The conditions are that you live together as a family, do nothing incompatible with the marriage, and pose no national security or public order obstacle. It applies to husbands and wives alike, and the law does not require you to live in Turkey. The three years run from the wedding, or from the date your spouse became Turkish if that was later.
Make sure the marriage is registered in the Turkish civil register now; if you married abroad, your spouse can register it at a Turkish consulate. If you want to live in Turkey meanwhile, a family residence permit as the spouse of a Turkish citizen is the usual route; it can be issued for up to three years at a time and needs proof of income, health insurance and housing.