  A stochastic magnetic field in the early Universe will produce anisotropies
in the temperature and polarization of the cosmic microwave background. We
derive analytic expressions for the microwave background temperature and
polarization power spectra induced by vector and tensor perturbations from a
power-law magnetic field. For a scale-invariant stochastic magnetic field
smoothed over a comoving scale of $1 {\rm Mpc}$, the MAP satellite has the
potential to constrain the comoving mean-field amplitude to be no greater than
approximately $2\times10^{-9}$ G. Limits improve as the power-law slope
increases: for causally-generated power-law magnetic fields, the comoving
mean-field amplitude has an upper bound of approximately $4\times10^{-13} {\rm
G}$. Such constraints will surpass all current limits on galactic-scale
primordial stochastic magnetic fields at decoupling.
