  Cosmological magnetic fields induce temperature and polarization fluctuations
in the cosmic microwave background (CMB) radiation. A cosmological magnetic
field with current amplitude of order $10^{-9}$ G is detectable via
observations of CMB anisotropies. This magnetic field (with or without
helicity) generates vector perturbations through vortical motions of the
primordial plasma. This paper shows that magnetic field helicity induces
parity-odd cross correlations between CMB temperature and $B$-polarization
fluctuations and between $E$- and $B$-polarization fluctuations, correlations
which are zero for fields with no helicity (or for any parity-invariant
source). Helical fields also contribute to parity-even temperature and
polarization anisotropies, cancelling part of the contribution from the
symmetric component of the magnetic field. We give analytic approximations for
all CMB temperature and polarization anisotropy vector power spectra due to
helical magnetic fields. These power spectra offer a method for detecting
cosmological helical magnetic fields, particularly when combined with Faraday
rotation measurements which are insensitive to helicity.
