  A primordial magnetic field in the early universe will cause Faraday rotation
of the linear polarization of the cosmic microwave background generated via
Compton scattering at the surface of last scattering. This rotation induces a
non-zero parity-odd (B-mode) polarization component. The Wilkinson Microwave
Anisotropy Probe (WMAP) 5-year data puts an upper limit on the magnitude of the
B-polarization power spectrum; assuming that the B-polarization signal is
totally due to the Faraday rotation effect, the upper limits on the comoving
amplitude of a primordial stochastic magnetic field range from $6 \times
10^{-8}$ to $2 \times 10^{-6}$ G on a comoving length scale of 1 Mpc, depending
on the power spectrum of the magnetic field.
