The selected answer uses the most common method answered to this and similar questions. However, it did not work for me with both front and back cameras on Samsung. For those needing another solution which works across both front and back cameras for Samsung and other major manufacturers, this answer by nvhausid is awesome:
https://stackoverflow.com/a/18915443/6080472
For those who don't want to click through, the relevant magic is to use the CameraInfo rather then relying on EXIF or a Cursor over the media files.
Bitmap realImage = BitmapFactory.decodeByteArray(data, 0, data.length);
android.hardware.Camera.CameraInfo info = new android.hardware.Camera.CameraInfo();
android.hardware.Camera.getCameraInfo(mCurrentCameraId, info);
Bitmap bitmap = rotate(realImage, info.orientation);
Full code in the link.