That is the wrong lens for your camera. The Nikon 12-24mm F/4 is an excellent lens but it is designed for a crop sensor. Nikon calls those DX lenses.
Luckily, Nikon makes an even more fantastic lens for your camera, the Nikkor 14-24mm F/2.8 which they call an FX lens. It will give you a wider angle of view, brighter aperture and is very sharp.
If you enable DX crop mode on the D800, then the vignette will disappear because the camera will crop the image for you which results in an obviously reduced resolution and angle-of-view, pretty much wasting a good part of what you probably paid for the D800.