Yes this can be done but you have to act smart for this one thing. Now if you want a user to be editor then visit his profile and edit his profile and make his editor. Now if you want some specific privileges then go in admin section and then on permissions page see what permissions you want to give to an editor and then save all the results.
But keep in mind that this will give those permissions to all the editors on your website. There is no other way to give specific privileges to a person.