Enqueue a script which uses a jquery ui datepicker http://jqueryui.com/datepicker/

gistfile1.txt

add_action( 'wp_enqueue_scripts', 'custom_enqueue_datepicker' );

function custom_enqueue_datepicker() {
	// Optional - enqueue styles
	wp_enqueue_style( 'jquery-ui', 'http://ajax.googleapis.com/ajax/libs/jqueryui/1.8.21/themes/smoothness/jquery-ui.css', false, '1.0', false );
	
	// Enqueue YOURTHEME/js/datepicker.js
	wp_enqueue_script(  'your-datepicker-script', get_stylesheet_directory_uri() . '/js/datepicker.js', array( 'jquery', 'jquery-ui-datepicker' ), '1.0', true );
}