The interference of two particles is a major pillar of quantum mechanics, very much like the phenomenon of single particle interference. The former is observed through the joint probability
of finding two particles, emitted from two spatially separated and uncorrelated sources, at two separate detectors. Such interference has been observed with photons in the historical Hanbury
Brown and Twiss (HBT) experiment, and later with electrons. Condensed matter systems operating in the quantum Hall regime can exhibit emergent particles (dubbed anyons) with exotic fractional statistics. Despite intensive study, direct signatures of anyonic statistics remain elusive; their entanglement has not been demonstrated. Here we study an HBT interferometer with anyons, which can directly probe entanglement and fractional statistics of initially uncorrelated particles. Specically, we calculate HBT cross-correlations of Abelian Laughlin anyons. The  correlations exhibit partial bunching (like bosons), rather than anti-bunching (like fermions), indicating a substantial statistical transmutation from the underlying electronic degrees of freedom. Furthermore, there are qualitative differences between the anyonic signal and the corresponding bosonic or fermionic signals, which indicate that anyons cannot be thought of as simply intermediate between bosons and fermions. Our analysis is an important step towards mapping the statistical correlations of a broad spectrum of quasiparticles, including non-Abelian anyons.