We present a full evaluation of the deeply virtual Compton scattering cross section in the dipole framework in the small- x region. The result features the cosϕ and cos2ϕ azimuthal angular correlations, which have been missing in previous studies based on the dipole model. In particular, the cos2ϕ term is generated by the elliptic gluon Wigner distribution of which the measurement at the planned electron-ion collider provides important information about the gluon tomography at small x. We also show the consistency with the standard collinear factorization a...