Hi boracasli, we'd be happy to support Turkish, we just need someone to add rules and test them. There's an old version of LanguageTool with support for Turkish at https://code.google.com/p/garniturk/, so a first step might be to port the rules from the old version to the current version of LT.
There's an introduction at http://wiki.languagetool.org/development-overview. As you cannot yet select "Turkish" in LT, you could try out those rules by adding them to the "grammar.xml" file of some other language as a test.
Could you tell us more about your background, are you a developer? Have you worked with XML?