There is a plugin for that here, but I have issues with it. I use it to search for product categories, of which I have over 6,200. I would guesstimate that it fails to find the category(ies) I’m searching for about 30% of the time. Also, it isn’t verified to be completely successful with the current WordPress version.
A better alternative for you might be to use one of the taxonomy filter plugins. They filter the category list as you type. The one I’m currently using, and having success with, is here.
Good luck to you in finding what you’re looking for.