The seismic scattering attenuation in randomly inhomogeneous media is successfully explained by a Born approximation-based theory, established by R. S. Wu and H. Sato. The key is to eliminate the contribution of forward scattering within a cutoff scattering angle (CSA) when evaluating the scattering attenuation in order to avoid overestimating attenuation at high frequencies. The value of the CSA is, however, not objectively determined in the theory, and the choice of it remains an open question. We investigate the constraint by causality on the choice of the CSA for random acoustic media with constant densities. On the basis of the Kramers-Kr¿nig relation, we derive simple relations of the phase velocities in the high- and low-frequency limits with the CSA. We further discuss the probable values of the CSA on the basis of a thought experiment. Surprisingly, they are independent of the details of inhomogeneities.