  We propose a standard time-of-flight experiment as a method for observing the
anyonic statistics of quasiholes in a fractional quantum Hall state of
ultracold atoms. The quasihole states can be stably prepared by pinning the
quasiholes with localized potentials and a measurement of the mean square
radius of the freely expanding cloud, which is related to the average total
angular momentum of the initial state, offers direct signatures of the
statistical phase. Our proposed method is validated by Monte Carlo calculations
for $\nu=1/2$ and $1/3$ fractional quantum Hall liquids containing a realistic
number of particles. Extensions to quantum Hall liquids of light and to
non-Abelian anyons are briefly discussed.
