Rewrite URL Parameter And Force ‘Pretty’ Permalink

You could force the redirect this way by checking for the get_var query value:

add_action('init','my_redirect_check');
function my_redirect_check() {
    if (isset($_GET['my_var'])) {
        if ($_GET['my_var'] != '') {
            if ($_SERVER["HTTPS"]) {$location = 'https://';}
            else {$location = 'http://';}
            $location .= $_SERVER['SERVER_NAME'];   
            $location .= strtok($_SERVER['REQUEST_URI'],'?');
            $location = trailingslashit($location);
            $location .= $_GET['my_var'];
            $location = trailingslashit($location);                          
            wp_redirect($location); exit;
        }
    }
}

Note: you will lose any other querystring values this way, but you could always rebuild and append those also if needed.