Since 1966, till 2009, between 67,741 and 53,960 people have received BA/BS in archaeology or anthropology degrees, in the United States, with a concentration in archaeology (thus the term archaeology-based degree). During that same period between 9,546-11,769 MA and 3,921-4,598 PhD were also earned. Add in the 4000+ BA/BS earned in 2010 and 2011 you have roughly 70,000 people with at least a undergraduate degree in archaeology. Between 1944-2009 it is actually 69,552 so roughly 75,000 people with a undergraduate degree. Furthermore, not everyone who obtained a MA or PhD undertook an archaeology BA so the total number of people with a Archaeology-based degree could be higher (AA were not counted either).
The data is from the American Anthropology Association (personal correspondence), the National Science Foundation, and the National Center for Education Statistics. There are some difference in the numbers provided by the different between data sources that as of yet can not be explained.
How were these numbers obtained? By taking the number of Anthropology degrees earned during that time, of which archaeology degrees are a sub-section, and multiply it by 25%, the rough number of anthropology degrees that concentrate on archaeology. Which means these numbers are not exact but estimations of the numbers earned.