Turkey has some great delivery services. The best service for ordering food in is: http://ankara.yemeksepeti.com/
This website has hundreds of restaurants in Ankara listed, complete with menus. You can order directly online without speaking to anyone and choose when you want the food to arrive. When you first register, they will call you to confirm your account and speak some English. After that, your account is activated.
For groceries, Migros has a large delivery service in Ankara. You can order online at www.migros.com.tr. Once you enter the website, click on "sanal market" and then choose your city. There is an English version of the online market, although the food names and ingredients are often not translated.