Do I have to be enrolled in an anthropology department to apply?
No. You can apply regardless of departmental affiliation. However, funding decisions are made on the basis of the potential of the project to make a significant contribution to the field of theoretical anthropology. You must clearly demonstrate this potential in your application and also show a good knowledge of the relevant anthropological literature. It is not sufficient to merely use anthropological techniques (e.g. participant observation) to carry out research in your own disciplinary area or to carry out research in a non-western setting.