  We study Delbr\"uck scattering in a Coulomb field in the presence of a laser
field. The amplitudes are calculated in the Born approximation with respect to
the Coulomb field and exactly in the parameters of the laser field having
arbitrary strength, spectral content and polarization. The case of high energy
initial photon energy is investigated in detail for a monochromatic circularly
polarized laser field. It is shown that the angular distribution of the process
substantially differs from that for Delbr\"uck scattering in a pure Coulomb
field. The value of the cross section under discussion may exceed the latter at
realistic laser parameters that essentially simplify the possibility of the
experimental observation of the phenomenon. The effect of high order terms in
the quantum intensity parameter $\chi$ of the laser field is found to be very
important already at relatively small $\chi$.
