Hi and welcome to LQ,
I don't think it's wise to allow ftp user creation without approval.
That said, there is proma
that is a php application that allows users to apply for ftp permission through a web form and stores their data in a mysql database. But it needs a final approval from an administrator (not necessarily the root), so it's not exactly what you're looking for.
Also the app is quite aged, so there is a chance it doesn't work with newer php/mysql versions