  In this paper, we show the possibility of recovering a sum of Dirac measures
on the rotation group $SO(3)$ from its low degree moments with respect to
Wigner D-functions only. The main Theorem of the paper states, that exact
recovery from moments up to degree $N$ is possible, if the support set of the
measure obeys a separation distance of $\frac{36}{N+1}$. In this case, the
sought measure is the unique solution of a total variation minimization. The
proof of the uniqueness requires localization estimates for interpolation
kernels and corresponding derivatives on the rotation group $SO(3)$ with
explicit constants.
