  Poincar\'e Gauge Theories are a class of Metric-Affine Gravity theories with
a metric-compatible (i.e. Lorentz) connection and with an action quadratic in
curvature and torsion. We perform an explicit one-loop calculation starting
with a single term of each type and show that not only are all other terms
generated, but also many others. In our particular model all terms containing
torsion are redundant and can be eliminated by field redefinitions, but there
remains a new term quadratic in curvature, making the model non-renormalizable.
We discuss the likely behavior of more general theories of this type.
