The ground state of an acceptor-bound hole in a zinc-blende semiconductor is formed by four eigenstates of the total angular momentum, which is a vector sum of spin and orbital moment of the hole. As a result, the hyperfine interaction of the hole with lattice nuclei becomes anisotropic and coordinate dependent.We develop a theory of dynamic polarization of nuclear spins by the acceptor-bound hole, giving full account for its complex spin structure. The rate of hole-nuclear flip-flop transitions is shown to depend on the angle between the total angular momentum of the hole and the position vector of the nucleus with respect to the acceptor center. The resulting spatially inhomogeneous spin polarization of nuclei gives rise to nonequidistant spin splitting of the hole, which can be detected by methods of optical or microwave spectroscopy.