You don’t declare the order of the results when you register the post type.
Instead, you do at the time the results are requested. If you’re using WP_Query to get the results then you add your orderby and order arguments to the request.
http://codex.wordpress.org/Class_Reference/WP_Query
If you want to change the order of the results on the archive pages such as http://www.yoursite.com/calendar/ then you have to filter the existing query by can using the pre_get_posts filter like so:
function wpse_167441_reorder_calendar($query) {
if ( !is_admin() && $query->is_main_query() ) {
if (is_post_type_archive('calendar')) {
$query->set('orderby', 'date' );
$query->set('order', 'ASC' );
}
}
}
add_action('pre_get_posts','wpse_167441_reorder_calendar');
If you want this to be the case in the admin area too then you can remove the !is_admin check. Be sure to test that you have not effected other post types when you’re doing this – that’s why the is_post_type_archive condition is in there.
http://codex.wordpress.org/Plugin_API/Action_Reference/pre_get_posts
Hope that’s what you were after.