eXtream Software Development has released their real-time vocal pitch correction plug-in, Vocal Tune PRO for iOS. As an Audio Unit and IAA plug-in, it can be used in your favourite DAW to auto tune your vocals or other monophonic audio.
After selecting the right key and scale, set the retune amount and retune speed to adjust between a natural effect or a more processed/robotic effect as can be heard in modern productions. To bring some life back to heavily auto tuned melodies, you can add artificial vibrato with settings for the vibrato depth, rate, time between the start of a note and the onset of vibrato and the time it takes for the vibrato to reach full depth.
Vocal Tune PRO comes as an Audio Unit plug-in and must be run inside a host app such as Audio Evolution Mobile Studio, Auria Pro, Cubasis, etc. supporting AU Music Effects (audio effects + MIDI). Although you can run it stand-alone as a real-time effect with mic input, it's best to use it within host software.
The app is free to download and has a 3-day trial. During this trial, silence will be played occasionally. To unlock full functionality, an in-app purchase is required ($6.99).