  A primordial cosmological magnetic field induces and supports vorticity or
Alfven waves, which in turn generate cosmic microwave background (CMB)
anisotropies. A homogeneous primordial magnetic field with fixed direction
induces correlations between the $a_{l-1,m}$ and $a_{l+1,m}$ multipole
coefficients of the CMB temperature anisotropy field. We discuss the
constraints that can be placed on the strength of such a primordial magnetic
field using CMB anisotropy data from the WMAP experiment. We place 3 $\sigma$
upper limits on the strength of the magnetic field of $B < 15$ nG for vector
perturbation spectral index $n=-5$ and $B<1.7$ nG for $n=-7$.
