  The Weyl semimetal is characterized by three-dimensional linear band touching
points called Weyl nodes. These nodes come in pairs with opposite chiralities.
We show that the coupling of circularly polarized photons with these chiral
electrons generates a Hall conductivity without any applied magnetic field in
the plane orthogonal to the light propagation. This phenomenon comes about
because with all three Pauli matrices exhausted to form the three-dimensional
linear dispersion, the Weyl nodes cannot be gapped. Rather, the net influence
of chiral photons is to shift the positions of the Weyl nodes. Interestingly,
the momentum shift is tightly correlated with the chirality of the node to
produce a net anomalous Hall signal. Application of our proposal to the
recently discovered TaAs family of Weyl semimetals leads to an
order-of-magnitude estimate of the photoinduced Hall conductivity which is
within the experimentally accessible range.
