How difficult would it be for a person with a Ph D in anthropology to get a job as an anthropology or archaeology professor?

To use the old cliche, "it just depends."

Experience teaching/lecturing/tutoring during your post-grad helps, as does publishing regularly and attending conferences. But as with most cool jobs there are way more people qualified than there are jobs available.

Other than that it might help to kiss up to the other professors in the department. That seems to work quite well where I come from... :P