A theory of a second-order mechanism giving two-magnon electric dipole absorption in rutile structure antiferromagnets is developed. In the mechanism, the absorption arises from indirect coupling of the spins to the field through the infrared-active optical phonons via the exchange-strictive part of the spin-phonon interaction. Detailed expressions are derived for the constants in the phenomenological Hamiltonian used by Allen et al. in interpreting experiments on a two-magnon electric dipole absorption recently observed in MnF2 at 110 cm-1. Thus, the frequency, temperature dependence, and electric dipole character of the observed line are predicted. To further compare the theory with the MnF2 experiments, a model for the exchange interactions is postulated which gives an expected line shape and magnetic field dependence which are consistent with observations. A very imprecise intensity estimate is also consistent with experiment. The question of the choice between this mechanism and another proposed for the MnF2 line and involving the interaction of the field with the exchange via the perturbation of the electronic orbitals is discussed.