App Recommendation for automatically stitching screenshots together on iOS
AutoStich Panorama
...has been my choice for the iPhone. You still need to take the pictures manually fist. You can choose all the pictures which you want to stich from your camera roll.

up to 18 megapixels are supported for stitched panoramas
camera images in any order or arrangement (vertical, horizontal, mixed).
option to stich using high res images for better result