  We estimate the depolarizing effect of a primordial magnetic field upon the
cosmic microwave background radiation due to differential Faraday rotation
across the last scattering surface. The degree of linear polarization of the
CMB is significantly reduced at frequencies around and below 30 GHz $(B_*
/10^{-2}{\rm Gauss})^{1/2}$, where $B_*$ is the value of the primordial field
at recombination. The depolarizing mechanism reduces the damping of
anisotropies due to photon diffusion on small angular scales. The $l\approx
1000$ multipoles of the CMB temperature anisotropy correlation function in a
standard cold dark matter cosmology increase by up to 7.5\% at frequencies
where depolarization is significant.
