Your question mentions date and year so I it seemed like UIDatePickerModeDate would suffice but as you are looking for month and year which is not an available option. I suggest you consider using a two component UIPickerView object.
Original Answer
You can do this by changing the Mode property under Date Picker to Date in the Attributes Inspector in the right bar ( Cmd + Option + 4 ). You can also do this programmatically,
datePicker.datePickerMode = UIDatePickerModeDate;