The PR that you have linked to adds a delete_category method to the Discourse API gem. If you are using the Discourse API gem for your API calls, you will be able to use that method. If you are not using the Discourse API gem, you can delete a category through the API by making a DELETE request to your site’s /categories/<category_id> route. Set <category_id> to the id of the category you are wanting to delete.
I believe that either with the API gem, or with the DELETE request made to /categories/<category_id>, an error will be returned if the category has any topics in it other than the initial “About” topic that was created when you first created the category. You need to recategorize a category’s topics before deleting the category.