Android spinner with date picker, like Google Calendar app

Twaddington’s comment on his answer is actually the right approach.
What you need is to create a text view and apply the style

style="@android:style/Widget.DeviceDefault.Light.Spinner"

Then you can create a click listener on the text view and use it to open a DatePickerDialog. That can be accomplished as shown here: https://stackoverflow.com/a/8127571/332738
(If you follow the example, remember to add a default constructor to DatePickerDialogFragment so that your app does not crash on rotate)