A mirror won't do the job as it would interfere with the picture. A better solution is a view screen on the digital camera much as on a video camera that can be turned to show what is being captured.

I don't think too many people would be willing to trade off "size" in respect of this type of camera. For the mirror to be useful you would need a mirror about the size of a half a sheet of paper to capture the reflection of your face at an arm's length.

Well then instead of a mirror on the digital cameras you could be able to turn the screen to see yourself like on camcorders

Actually, you could make the mirror convex, like the little round mirrors that are stuck onto truck mirrors to give a wide view. This enable the mirror to be small enough to fit on the camera. However, this wouldn't necessarily give you an accurate indication of what the image will look like due to parallax. Really, any mirror used for this purpose will have a parallax problem. What I mean by that is if you look straight at the mirror the image could be centered in the camera, but if you angle the camera slightly, say to show more of your body, than the mirror image will be lower than the camera is actually pointing. It would be better to have a LCD view screen that could be flipped around the side of the camera.

You mean exactly like the mirrors that are already there on mobiles?