There is no way in the Episerver CMS UI to move a category from under its parent, essentially you're limited to reordering categories within the existing structure. This is a problem we recently ran up against when editors needed to restructure a large category hierarchy.
There is, of course, always the option to do this directly in the database as outlined by Nicola Ayan in a recent blog post. However, this isn't necessarily practical if you've got a large number of categories to move and can also create the impracticable situation where editors have to document all the categories to move and then hand-off the task to a dev who'll write (and execute) the SQL script.
My solution (as you've maybe guessed from the blog title?) was to throw together a quick (and not overly attractive) plugin that allows editors to move categories:
You can find the complete source code in a Gist here.
Depending on your requirements and taxonomy complexity I'd also definitely recommend taking a look at Geta's EpiCategories which stores categories as content and comes with some nice enhancements. There's even a great blog post on migrating from Episerver Categories to EpiCategories.