  We report a systematic investigation of dc magnetization and ac
susceptibility, as well as anisotropic magnetocaloric effect in bulk CrI$_3$
single crystals. A second-stage magnetic transition was observed just below the
Curie temperature $T_c$, indicating a two-step magnetic ordering. The low
temperature thermal demagnetization could be well fitted by the spin-wave model
rather than the single-particle model, confirming its localized magnetism. The
maximum magnetic entropy change $-\Delta S_M^{max} \sim 5.65$ J kg$^{-1}$
K$^{-1}$ and the corresponding adiabatic temperature change $\Delta T_{ad} \sim
2.34$ K are achieved from heat capacity analysis with the magnetic field up to
9 T. Anisotropy of $\Delta S_M(T,H)$ was further investigated by isothermal
magnetization, showing that the difference of $-\Delta S_M^{max}$ between the
$ab$ plane and the $c$ axis reaches a maximum value $\sim$ 1.56 J kg$^{-1}$
K$^{-1}$ with the field change of 5 T. With the scaling analysis of $\Delta
S_M$, the rescaled $\Delta S_M(T,H)$ curves collapse onto a universal curve,
indicating a second-order type of the magnetic transition. Furthermore, the
$-\Delta S_M^{max}$ follows the power law of $H^n$ with $n = 0.64(1)$, and the
relative cooling power RCP depends on $H^m$ with $m = 1.12(1)$.
