I've worked a good bit as a photographer of archaeology in Israel. My experience is that if you are a good photographer, and are willing to do a little research and learning on your own, you can probably sign on as a photographer in any number of digs during the course of a summer (most are in the summer, because that's when college kids are available as cheap labor.)
I don't know anything about meso-American or European archaeology, and the opportunities may be fewer there. However, if you're interested in the Holy Land, go out to a big newsstand right now and look for the Biblical Archaeology Review (which is not a religious publication, but covers archaeology in the lands of the Bible, which mostly means Israel, with some stuff from Jordan, Egypt, Syria and Lebanon.) The current issue is the "dig" issue, which lists all (or most) of the Holy Land digs which are looking for volunteers this year. You could write to any of them -- virtually all of them will be on the web -- and ask if they need a photographer.
Big catch: you'll be a "volunteer," and that usually means you'll have to pay your own way, including room and board. Probably cost you $3,000 for the summer, including air fare, but it's a heck of a way to see the area, and hang out with some really great archaeologists, and learn the job.
All the photography, as far as I know, has switched to digital, so you'd need a couple of digital cameras, lenses and a couple of flashes.
The job can be brutal -- bad light, finicky diggers, wierd subjects (think about trying to show different layers of brown dirt in a big brown dirt wall, in bad light.) Where I've dug, light control is critical -- and you use shades and various invented-on-the-spot light modifiers as often as you use standard equipment. You also have to be exceptionally responsible. After you shoot something -- the photography always comes last -- the subject is then either removed from its context (artifacts) or destroyed (the floor you're documenting) and you can never get it back. If the pictures are messed up, it's an extremely serious matter.
The situation in archaeology is quite different than that of anthropology, if I understand the above postings correctly (I don't know anything about anthropology.) For one thing, the subject matter is usually totally inert, and you mostly only shoot what the dig director or area directors want you to shoot...and the publicity shots you shoot are always with the approval of the volunteers who appear in the photos (and who are almost always happy to be in them.)
If you have any specific questions, I'd be glad to answer them...but if you're a good photographer, and are willing to learn a bit more about the specifics of field archaeology, it can be an interesting way to see the world.
If you want to see the kind of shots archaeological photographers are expected to shoot, browse through this web site, where I've done quite a bit of the pre-2005 photography, not including the aerials (I wanted to dig in 2005, rather than shoot):
www.rehov.orgJC