  The possibility of nonnegligible $W$ electric dipole ($\widetilde{\mu}_W$)
and magnetic quadrupole ($\widetilde{Q}_W$) moments induced by the most general
$HWW$ vertex is examined via the effective Lagrangian technique. It is assumed
that new heavy fermions induce an anomalous CP-odd component of the $HWW$
vertex, which can be parametrized by an $SU_L(2)\times U_Y(1)$-invariant
dimension-six operator. This anomalous contribution, when combined with the
standard model CP-even contribution, lead to CP-odd electromagnetic properties
of the $W$ boson, which are characterized by the form factors $\Delta
\widetilde{\kappa}$ and $\Delta \widetilde{Q}$. It is found that $\Delta
\widetilde{\kappa}$ is divergent, whereas $\Delta \widetilde{Q}$ is finite,
which reflects the fact that the latter cannot be generated at the one-loop
level in any renormalizable theory. Assuming reasonable values for the unknown
parameters, we found that $\widetilde{\mu}_W\sim 3-6\times 10^{-21}$ e-cm,
which is eight orders of magnitude larger than the SM prediction and close to
the upper bound derived from the neutron electric dipole moment. The estimated
size of the somewhat less-studied $\widetilde{Q}_W$ moment is of the order of
$-10^{-36}$ e-cm^2, which is fifteen orders of magnitude above the SM
contribution.
