  We consider the wave equation for spinors in ${\cal D}$-dimensional Weyl
geometry. By appropriately coupling the Weyl vector $\phi _{\mu}$ as well as
the spin connection $\omega _{\mu a b } $ to the spinor field, conformal
invariance can be maintained. The one loop effective action generated by the
coupling of the spinor field to an external gravitational field is computed in
two dimensions. It is found to be identical to the effective action for the
case of a scalar field propagating in two dimensions.
