  Many-body localization (MBL) has been widely investigated for both fermions
and bosons, it is, however, much less explored for anyons. Here we numerically
calculate several physical characteristics related to MBL of a one-dimensional
disordered anyon-Hubbard model in both localized and delocalized regions. We
figure out a logarithmically slow growth of the half-chain entanglement entropy
and an area-law rather than volume-law obedience for the highly excited
eigenstates in the MBL phase. The adjacent energy level gap-ratio parameter is
calculated and is found to exhibit a Poisson-like probability distribution in
the deep MBL phase. By studying a hybridization parameter, we reveal an
intriguing effect that the statistics can induce localization-delocalization
transition. Several physical quantities, such as the half-chain entanglement,
the adjacent energy level gap-ratio parameter, {\color{black} the long-time
limit of the particle imbalance}, and the critical disorder strength, are shown
to be non-monotonically dependent on the anyon statistical angle. Furthermore,
a feasible scheme based on the spectroscopy of energy levels is proposed for
the experimental observation of these statistically related properties.
