There is a paid extension from Taifun that does this (actually not completely paid, there is a free part and a paid part, but your requirements need the paid part).
Get current ringtone. Type can be RINGTONE, NOTIFICATION or ALARM. Thank you James and chabooya for being the sponsors of this method.
Note: as Triratna found out here: after setting another ringtone outside of the app (for example in the default ringtone app), the extension does not refresh and still will display the previously set ringtone. As workaround, restart your app to get the correct ringtone
