Will sigma 170-500mm autofocus with nikon d7000?

Will sigma 170-500mm autofocus with nikon d7000?

Sure. As long as you get it in Nikon mount.

I would advice you to see if you can afford a new 150-500.It's a better designed lens and you'd get HSM for quicker focussing and a decent optical stabilizer

Yes, unlike the D3100 and D5100 the D7000 has an AF motor in the body, an as such will work with this lens.

A Nikon mount version will work fine. I'm currently using a Sigma 135-400mm lens and it autofocuses perfectly on all of my Nikon DSLR's and SLR's. The entry-level Nikons (D40-D5100) won't work with this lens at this Sigma isn't an HSM model.