  We report the calculation of the isovector CP-odd $\pi N$ interaction
generated by the Weinberg operator, the CP violating three-gluon operator. This
enables to restrict models which induce the operator by using experimental data
of atomic electric dipole moment. The QCD sum rules are used to determine the
matrix element required to assess the CP-odd $\pi N$ interactions. The relation
between the Weinberg operator and the Hg and Xe EDMs is clarified, and the
constraint on the Weinberg operator is obtained using the experimental data for
the Hg EDM.
