The easiest way to do that would be to use a WordPress membership plugin so that users who have access to private categories on Discourse also have access to members-only pages on the WordPress site. Then the links to the private Discourse categories could be added to the private WordPress pages.
If the WordPress site isn’t setup that way, it would still be possible to do it, but it would require some custom code.
I’m working on a plugin that connect the WishList Member WordPress plugin to the WP Discourse plugin. I’ll try to get a basic version of that finished this weekend. I think it would do what you are looking for, but it would require buying the WishList Member plugin. If you’re thinking of doing that, wait a couple of days until I have it finished and can confirm that it does what you’re looking for.