  Pursuing the exotic quantum spin liquid (QSL) state in the Kitaev material
$\alpha$-RuCl$_3$ has intrigued great research interest recently. A fascinating
question is on the possible existence of field-induced QSL phase in this
compound. Here we perform a high-field measurement of the magnetization process
of $\alpha$-RuCl$_3$ up to 102 T employing the non-destructive and destructive
pulsed magnets. Under the out-of-plane field along the c$^*$ axis (i.e.,
perpendicular to the honeycomb plane), two quantum phase transitions are
uncovered at respectively 36 T and about 83 T, between which there lies an
intermediate phase as the predicted QSL. By measuring the magnetization data
with fields tilted from the c$^*$ axis up to $90^\circ$ (i.e., in-plane
direction), we obtain the field-angle phase diagram that contains the zigzag,
paramagnetic, and QSL phases. Based on the accurate
$K$-$J$-$\Gamma$-$\Gamma^{\prime}$ model of $\alpha$-RuCl$_3$, we perform
density matrix renormalization group simulations and reproduce the quantum
phase diagram in excellent agreement with experiments.
