  In a previous paper \cite{Hatta:2020ltd}, we have pointed out the connection
between the $CP$-odd three-gluon (Weinberg) operator and certain twist-four
corrections in polarized deep inelastic scattering. Based on this observation,
we give a numerical estimate of the electric dipole moment of the proton and
neutron induced by the Weinberg operator. Our result is smaller than the
previous estimates based on QCD sum rules by a factor of about 3 or more.
