How to make a custom alarm sound on iPhone

Yes you can do it with GarageBand For iOS.Record your voice and create a ringtone with it...

I Do that then you have the option of use it as standard ringtone and it appear in the ringtones section in settings sound so you can even create one for each contact or alarm or sounds etc ....

You would need to do so on a computer and then import the ring tone to the device via iTunes.

alternately, you can purchase tones from the iTunes store directly from the app, or set it to use any song you have in the Music app..