  We calculate the nucleon matrix element of Weinberg's dimension-6 CP-odd
gluon operator $f^{abc} (\tilde F_{\mu\nu})^a (F^{\mu\rho})^b
(F^{\nu}_{\;\;\rho})^c$ in the instanton vacuum. In leading order of the
instanton packing fraction, the dimension-6 operator is effectively
proportional to the topological charge density $(\tilde F_{\mu\nu})^a
(F^{\mu\nu})^a$, whose nucleon matrix element is given by the flavor-singlet
axial charge and constrained by the $U(1)_A$ anomaly. The nucleon matrix
element of the dimension-6 operator is obtained substantially larger than in
other estimates, because of the strong localization of the nonperturbative
gluon fields in the instanton vacuum. We argue that the neutron electric dipole
moment induced by the dimension-6 operator is nevertheless of conventional
size.
