Some of my mentors, none of whom are in anthropology departments, prefer to say "trained as an anthropologist, so-and-so investigates…" when describing people in the field, as opposed to saying "so-and-so is an anthropologist." If you are on the job market this may be hard to do as you are likely to have just become a Ph.D.-wielding anthropologist, and to be quite proud of the moniker and achievement. But the shift in self-definition is important for you and your future academic home, I would argue.
I just went through the whole job-hunting process before signing a contract to become a lecturer in media and cultural studies in the Sociology Department at Lancaster University, in Britain. I was able to apply for a silly number of jobs, get a bunch of interviews and campus visit requests, and have some choices and grounds on which to do some humble negotiating. I think my trick was post-disciplinary research and (a considerable amount of) cross-disciplinary publishing. I could apply to communications; media studies; anthropology; information studies; science, technology and society; sociology; television studies; American studies and Internet studies. If I were desperate I could apply for archaeology and film production positions. Postdoctoral positions, particularly those financed by the Mellon Foundation, are all about interdisciplinarity, as are jobs looking for digital humanities scholars.
So I’d encourage my fellow freshly minted A.B.D.s and Ph.D.s to begin seeing their research and their teaching across at least four or five large disciplines. Be able to realistically apply to four or five departments. One can put this together variously by publishing in different journals, collaborating with colleagues from different fields, or simply working the boundaries of one’s discipline in necessarily interdisciplinary ways. (All I can say is that I hope this is not my internalization of the precarity of neoliberal governmentality in the education sector.)
And there is something said for responding (in non-trendy and timeless ways!) to emergent patterns in industry, politics, and social movements. The departments recognize that what is in the news is what the students want to study. In my case this amounted to a recursive loop from the hype surrounding new media – Arab Spring, Anonymous, Wikileaks, SOPA, PIPA, and Occupy – to departments requesting applicants with expertise in social media and political movements. Oddly enough, if the academic job thing doesn’t work out, this type of preparation in the now prepares oneself better for a post-academic profession. In academe the joy of investigating emergent practices is that there is no syllabus. You get to design your own. And in the classroom you are not pulling teeth: the issues are on students' minds. It is relevant.
I may sound heretical to some of you by suggesting that post-anthropological disciplinary affiliations are necessary. But one gains much less than one loses by fundamentally aligning oneself with the orthodoxy of a specific discipline. On one hand, the qualitative and critical social sciences are converging. Critical theory and ethnographic or textual methods run across all the disciplines above. On the other hand, replicating the discourses specific to a discipline is important for the survival of that discipline and I am glad some people are monogamously "physical anthropologists" or whatnot.
But my argument is that this practice of disciplinary orthodoxy is dangerously myopic for a discipline and puts the job-hunter in a situation with few options. And this advice may apply for many others in the social sciences and the humanities, not just those trained in anthropology. I preferred to bring scholarship from other disciplines to anthropology, and though it proved difficult to buck anthropological tradition by studying contemporary technoculture in America, it provided me a wider repertoire of skills that apparently translate into numerous disciplines and a blessed job offer.
Good luck! Tell us how it goes for you.