  We investigate the current-induced spin polarization in the two-dimensional
hole gas (2DHG) with the structure inversion asymmetry. By using the
perturbation theory, we re-derive the effective $k$-cubic Rashba Hamiltonian
for 2DHG and the generalized spin operators accordingly. Then based on the
linear response theory we calculate the current-induced spin polarization both
analytically and numerically with the disorder effect considered. We have found
that, quite different from the two-dimensional electron gas, the spin
polarization in 2DHG depends linearly on Fermi energy in the low doping regime,
and with increasing Fermi energy, the spin polarization may be suppressed and
even changes its sign. We predict a pronounced peak of the spin polarization in
2DHG once the Fermi level is somewhere between minimum points of two spin-split
branches of the lowest light-hole subband. We discuss the possibility of
measurements in experiments as regards the temperature and the width of quantum
wells.
