  Gravitational radiation that propagates through an inhomogeneous mass
distribution is subject to random gravitational lensing, or scattering, causing
variations in the wave amplitude and temporal smearing of the signal. A
statistical theory is constructed to treat these effects. The statistical
properties of the wave amplitude variations are a direct probe of the power
spectrum of the mass distribution through which the waves propagate. Scattering
temporally smears any intensity variations intrinsic to a source emitting
gravitational radiation, rendering variability on time scales shorter than the
temporal smearing time scale unobservable, and potentially making the radiation
much harder to detect. Gravitational radiation must propagate out through the
mass distribution of its host galaxy before it can be detected at the Earth.
Plausible models for the distribution of matter in an $L_*$ host galaxy suggest
that the temporal smearing time scale is at least several milliseconds due to
the gas content alone, and may be as large as a second if dark matter also
scatters the radiation. The smearing time due to scattering by any galaxy
interposed along the line of sight is a factor $\sim 10^5$ times larger.
Gravitational scattering is an excellent probe of matter on parsec and
sub-parsec scales, and has the potential to elucidate the nature of dark
matter.
