WordPress requires PHP & MySQL (and mod_rewrite or equivalent is very helpful to have, too), so if you’re running those on the machine where your unhosted website currently resides, you can run WordPress. If you’re not, you can’t.
You can install PHP and MySQL to run locally on just about any OS you can name — I’ve got them running on my Windows desktop machine and my desktop & laptop Linux installations. See, for example, XAMPP.