My 25 year old pole barn has a couple of poles that have sunk six to eight inches and I want to jack them up in place. Is there a jack designed for this purpose or a suggested method?

You will need to temporarily install support posts by jacking them up so you can repair the poles.
Jacking Up Your House By Yourself - Jack Up House by Self - DIY

Yes, they have house jacks, or a good hydraulic jack.

How high is the ceiling in that barn? Reason I'm asking is after you jack it up are you going to dig beside that pole and crete in a support pad?

If you have ceiling height for a Small Kubota or backhoe you can get under that beams post and lift it with the boom. Then Temp supports. Use the hoe to dig beside lifted post and crete under it. Of course the other option is release that post from the plate and add more post. This of course works if its accessible inside and exposed.

21boat is on the right track. So the post sank 8", how do you know its done settling?