Convert gregorian datepicker to persian datepicker in swift?

You need to set the calendar, not the dateFormat:

dateFormatter.calendar = NSCalendar(identifier: NSCalendarIdentifierPersian)

You would also have to set the locale property if you want the language to change:

dateFormatter.locale = NSLocale(localeIdentifier: "fa_IR")

Also, as the comment on the question notes, you're working with an NSDateFormatter, not a UIDatePicker in your code. Fortunately the answer is still correct; UIDatePicker also has a calendar property that you would set to accomplish this goal.

Swift 3:

As Charles A. Said DatePicker has a calendar property and you can use it to have persian datepicker or even :

datePicker.calendar = Calendar(identifier: .persian)
datePicker.locale = Locale(identifier: "fa_IR")