The authors investigate the coupling of classical and quantum fermion antisymmetric tensor fields with a gauge gravitational field. It is shown that within the general framework of the classical Einstein-Cartan theory, a new nonlinear fermion theory can be constructed which turns out to be the microscopic Weyssenhoff theory of a spinning fluid. The single- loop gravitational counterterms, the conformal stress tensor, and the axial vector current anomalies are exhibited. Finally the differences between the present theory and the usual Dirac spinor field approach is discussed.