There are a number of language schools in Istanbul that teach Turkish as a language for foreigners
You can choose from a wide range of options- short intensive lessons of a few hours every day or one-class-per-week type course spread over a few months. You can also choose between private one-on-one teaching or opt for a group session. This is ideal for foreigners also looking to grow and build a social network.
Click here for a list of some of the language schools in Istanbul along with contact details and costs.