Iron-acceptor impurity pairs, consisting of a positively charged iron ion trapped on an interstitial site in the vicinity of an ionized acceptor, in silicon were observed by electron paramagnetic resonance for all common acceptor dopants (B, Al, Ga, In). The Zeeman splittings of these pairs, to which both spin and orbital momenta contribute, cover the range between 1.1 and 6.4. An interpretation of these spectroscopic splitting factors is presented, which considers the effects of the crystal field - of cubic, axial, or lower symmetry - and of spin-orbit interaction on the 4F ground state of the iron ion in a (3d)7 configuration. It is concluded that the apparent quenching of the orbital angular momentum is not due to a dynamical Jahn-Teller effect, nor due to hybridization. Rather, it is proposed that a significant reduction, by about 80%, of the orbital magnetism arises from covalency.