  A primordial cosmological magnetic field induces Faraday rotation of the
cosmic microwave background polarization. This rotation produces a curl-type
polarization component even when the unrotated polarization possesses only
gradient-type polarization, as expected from scalar density perturbations. We
compute the angular power spectrum of curl-type polarization arising from small
Faraday rotation due to a weak stochastic primordial magnetic field with a
power-law power spectrum. The induced polarization power spectrum peaks at
arcminute angular scales. Faraday rotation is one of the few cosmological
sources of curl-type polarization, along with primordial tensor perturbations,
gravitational lensing, and the vector and tensor perturbations induced by
magnetic fields; the Faraday rotation signal peaks on significantly smaller
angular scales than any of these, with a power spectrum amplitude which can be
comparable to that from gravitational lensing. Prospects for detection are
briefly discussed.
