In this job, you have the power to confuse strangers about what you do by telling them you are an "anthropologist."
Oh, you wanted a genuine answer. Fine. Very few anthropologists are self-employed (about 8 percent are consultants), so for the most part you are going to be reporting to a superior of some kind, be it in a business, a research facility, a place of higher learning, or a federal agency. You will be acquiring and analyzing information, and there's a bit of power associated with that, we suppose. It is likely the teaching anthropologists who wield the most power. They have the power to mold minds. That's some X-men stuff right there.