That capability is now on my Nokia Lumia 920 with an app titled Nokia Cinemagraphs. As you may expect with that name it’s exclusive to Nokia and it’s one of a few camera related apps the company makes available. They appear as standalone apps but can also be activated through the lenses feature on Windows Phone 8.
Once the app is running you take a photo that generates a 15 frame-per-second file. The app then steps you through selecting an area to be animated. Editing the animated area is done simply by “rubbing” the screen area you require. You’re then ready to upload to SkyDrive for sharing with your friends and family. Facebook sharing is coming soon.
Once you get an eye for creating a cinemagraph you can have a lot of fun with it.