No, in normal circumstances this is handled by server-side code, such as PHP. If you are using a content management system, the system inserts that class when the page URL matches the link URL. You can do it manually on a static site, but it’s not very efficient. An alternative is to use CSS, as explained here:
There are some other solutions in that thread, too, which are worth a look. One is to highlight the links with JavaScript, though the downside of this is that it won’t work if the user has JS off.