Create a plugin with Calendar picker

jQuery Datepicker is included in WP Core, you can add it to your functions.php (for themes) or index.php (for plugins)

function styles_scripts() {
    wp_enqueue_script('jquery-ui-datepicker');
    // Enqueue some theme-roller or default style...
    wp_enqueue_style('jquery-style','http://ajax.googleapis.com/ajax/libs/jqueryui/1.8.2/themes/smoothness/jquery-ui.css'); 
}
add_action( 'wp_enqueue_scripts', 'styles_scripts', 11 );

Than in the HTML part where you need the datepicker

<input type="text" id="MyDate" name="MyDate" value=""/>

And finally in your Javascript

jQuery(document).ready(function() {
    jQuery('#MyDate').datepicker({
        dateFormat : 'dd-mm-yy'
    });
});

This code is not tested, I just typed it here and hope it work well, let me know if you need more information or correction.