There’s no concept of archiving categories at the moment, only individual topics.
The best way would probably be to change the permissions on the categories so only staff can see them (it’s the security tab in the category edit modal)… they’d effectively be archived because normal users wouldn’t be able to see or interact with them.
Otherwise you could create an “Archive” category and make it the parent category of the categories you want to archive. One big issue with that are subcategories. Discourse currently only allows one level of subcategory, so if the categories you want to archive have subcategories… you wouldn’t be able to keep that hierarchy when moving them into the “Archive” category.