welcome to the forum!
Yes, indeed it will. In fact, this is Tokina's new version of this lens with a built-in AF motor, so it will even AF on a D40, D40x, D60, D5000, D3000 etc.
Since the D7000 already has an AF motor, you can consider the older model without AF motor if you want to save money..or even look at the Tokina 11-16 without AF motor if you want to go wider and have a larger max aperture (F2.
With wide angle lenses like these, the AF often ends at infinity anyway. For real fast shooting of moving objects, going hyper focal with manual focus is often better. And for landscapes/cityscapes you often have a lot more time.
Good luck with your choice!