  We consider the one-loop renormalization of a real scalar field interacting
with a Dirac spinor field in curved spacetime. A general Yukawa interaction is
considered which includes both a scalar and a pseudoscalar coupling. The scalar
field is assumed to be non-minimally coupled to the gravitational field and to
have a general quartic self-interaction potential. All of the one-loop
renormalization group functions are evaluated and in the special case where
there is no mass scale present in the classical theory (apart from the fields)
we evaluate the one-loop effective action up to and including order $R^2$ in
the curvature. In the case where the fermion is massive we include a chiral
term in $\gamma_5$ and we show that although the $\gamma_5$ term can be removed
by a redefinition of the spinor field an anomaly in the effective action arises
that is related to the familiar axial current anomaly.
