I just checked and the link works. You can try the link inside the game. It's in the main menu in the upper right corner.
Sorry to hear about your experience. It sounds like the problem is somewhere on your end. Because people join Discord every day. I honestly haven't encountered this, but maybe you have some privacy settings that don't allow you to follow links. Or accept invitations to the Discord channel. Please check on a different device if you have such an option.