The majority of gamma-ray emission from galactic dark matter annihilation is likely to be detected as a contribution to the diffuse gamma-ray background. I show that dark matter substructure in the halo of the Galaxy induces characteristic anisotropies in the diffuse background that could be used to determine the small-scale dark matter distribution. I calculate the angular power spectrum of the emission from dark matter substructure for several models of the subhalo population and show that features in the power spectrum can be used to infer the presence of substructure. The shape of the power spectrum is largely unaffected by the subhalo radial distribution and mass function, and for many scenarios I find that a measurement of the angular power spectrum by Fermi will be able to constrain the abundance of substructure. An anti-biased subhalo radial distribution is shown to produce emission that differs significantly in intensity and large-scale angular dependence from that of a subhalo distribution which traces the smooth dark matter halo, potentially impacting the detectability of the dark matter signal for a variety of targets and methods.