A quantitative theory of the shallow acceptor ground state in cubic semimagnetic semiconductors in a magnetic field is presented. The spherical tensor operators and reduced matrix elements technique are used in order to solve variationally the eigenvalue problem. The exchange interaction incorporated into the Favalence band effective-mass Hamiltonian causes the non-monotonic behaviour of the acceptor ionisation energy as a function of magnetic field. This energy initially decreases and only then gradually increases with increasing magnetic field. The results enable the development of the four Zeeman-split sublevels of the acceptor ground state to be followed over the entire range of the magnetic field.