Mexico citizens - Ordinary, Service and Special passport holders are required to have visa to enter Turkey. Ordinary, Service and Special passport holders, with a valid Schengen, UK, Canada, Japan or US visas or residing in these countries, may get their three-month multiple entry visas for their travel to Turkey with tourisitic purposes at the Turkish border gates upon their arrival. Only diplomatic passport holders are exempted from visa for their travels up to 90 days.
Turkey has an online Turkish Visa Application System where you can apply for e-Visa online and pay your fees in a few minutes. Mexico citizens who meets the required criteria can obtain a visa on arrival or online at Turkish Visa Application System - https://www.evisa.gov.tr/en/apply/.