drupal jquery mobile datepicker cannot select year
You can use Date module which has several options regarding to your requirement. You can use date functionalities in your custom form. 

For example,

$form['body']['dob'] = array( 
  '#type' =&gt; 'date',
  '#title' =&gt; 'Date of Birth', 
);


will have options to select date, month and year.

If #type =&gt; 'date_popup', it  will popup with calendar which allows user to select date.

Check this link for more info date example