Yes, you can file form 4868, the "Application for Automatic Extension of Time to File a U.S. Individual Income Tax Return". Once you open TurboTax, you should select the question "Want More Time To File This Year?", to file an extension. If you already started a return it will include an option to extend an existing return and another option if you have not started a return.
You should follow the TurboTax instructions to complete requesting an extension.
