How to scroll to a shortcode-generated anchor

It’s not really a WordPress related question, but since it was simple I posted an answer for you.

You can scroll to your element by using jQuery. Check if the query var is set, if so, scroll to the element after the page has been loaded:

(function($){
    // Function to get the current query var
    function get_query_var(query) {
        if (!url) url = window.location.href;
        query = query.replace(/[\[\]]/g, "\\$&");
        var regex = new RegExp("[?&]" + query + "(=([^&#]*)|&|#|$)"),
            results = regex.exec(url);
        if (!results) return null;
        if (!results[2]) return '';
        return decodeURIComponent(results[2].replace(/\+/g, " "));
    }
    // Check if query var is set
    var myQuery = get_query_var('some_id');
    if ( myQuery ) {
        // Now do the scrolling
            $( 'html,body' ).animate({
                scrollTop: $("#div_id").scrollTop()
                },1000
            );
    }
})(jQuery);