  The existence of a primordial magnetic field at the last scattering surface
may induce a measurable Faraday rotation in the polarization of the cosmic
microwave background. We calculate the magnitude of this effect by evolving the
radiative transfer equations for the microwave background polarization through
the epoch of last scatter, in the presence of a magnetic field. For a
primordial field amplitude corresponding to a present value of $10^{-9}{\rm G}$
(which would account for the observed galactic field if it were frozen in the
pre-galactic plasma), we find a rotation angle of around $1^\circ$ at a
frequency of 30 GHz. The statistical detection of this signal is feasible with
future maps of the microwave background.
