App Recommendation for automatically stitching screenshots together on iOS

You can try using an app like Photosynth, which creates stitched images from a set of images. Unlike some apps that only stitch panorama left to right, this allows for both up-down and left-right, which makes it a good choice for your purpose.

Using the latest in computer vision techniques, you can not only make a panorama from left to right, but also up and down, enabling you to capture a full “sphere”.

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