Recent studies have shown that black holes can indeed have hair in gravitational theories beyond minimal Einstein gravity. The hair is associated with the axion and dilaton of string theory, whose gauge and gravitational structure is richer than the conventional, minimally coupled theory. The axion in this case also has a dual rôle as a dynamical degree of freedom of the torsion. In this paper we suggest that there is a large class of models for which a torsion may be transmuted to an axion, and black holes develop hair. Indeed we show that even a model as simple as QED on a torsionful background space-time gives rise to axionic hair. We discuss this phenomenon and its implications.