PHP
$args = array(
'orderby' => 'title',
'order' => 'ASC'
);
$categories = get_categories($args);
usort($categories, function($a, $b) {
return get_field("category_order", "category_".$a->term_id) - get_field("category_order", "category_".$b->term_id);
});
foreach($categories as $category) {
echo '<li><a href="' . get_category_link( $category->term_id ) . '" title="' . sprintf( __( "View all posts in %s" ), $category->name ) . '" ' . '>' . $category->name . '</a>' . ' ' . '(' . $category->count . ')' . '</li> ';
}