If you don’t want to edit the wp core files, just try this :
function get_archives_link_mod ( $link_html ) {
preg_match ("/href='(.+?)'/", $link_html, $url);
$requested = "https://{$_SERVER['SERVER_NAME']} {$_SERVER['REQUEST_URI']}";
if ($requested == $url[1]) {
$link_html = str_replace("<li>", "<li class='current'>", $link_html);
}
return $link_html;
}
add_filter("get_archives_link", "get_archives_link_mod");
Copy the code in your themes functions.php – this may not be the most elegant solution, but it works (for html lists only) … Have fun!