Primordial inhomogeneous magnetic fields of the right strength can leave a signature on the CMB temperature anisotropy and polarization .
Potentially observable contributions to polarization B-modes are generated by vorticity and gravitational waves sourced by the magnetic anisotropic stress .
We compute the corresponding CMB transfer functions in detail including the effect of neutrinos .
The shear rapidly causes the neutrino anisotropic stress to cancel the stress from the magnetic field , suppressing the production of gravitational waves and vorticity on super-horizon scales after neutrino decoupling .
A significant large scale signal from tensor modes can only be produced before neutrino decoupling , and the actual amplitude is somewhat uncertain .
Plausible values suggest primordial nearly scale invariant fields with B _ { \lambda } \sim 10 ^ { -10 } \text { G } today may be observable from their large scale tensor anisotropy .
They can be distinguished from primordial gravitational waves by their non-Gaussianity .
Vector mode vorticity sources B-mode power on much smaller scales with a power spectrum somewhat similar to that expected from weak lensing , suggesting amplitudes B _ { \lambda } \sim 10 ^ { -9 } \text { G } may be observable on small scales for a spectral index n \sim - 2.9 .
In the appendix we review the covariant equations for computing the vector and tensor CMB power spectra that we implement numerically .