We report magnetic and magnetic circular dichroism investigations of a binuclear Co(II) compound. The Hamiltonian of the system involves an isotropic exchange interaction dealing with the real spins of cobalt(II) ions, spin-orbit coupling, and a low-symmetry crystal field acting within the T-4(1g) ground manifold of each cobalt ion. It is shown that spin-orbit coupling between this ground term and the low-lying excited ones can be taken into consideration as an effective g factor in the Zeeman part of the Hamiltonian. The value of this g factor is estimated for the averaged experimental values of Racah and cubic ligand field parameters for high-spin cobalt(II). The treatment of the Hamiltonian is performed with the use of a irreducible tensor operator technique. The results of the calculation are in good agreement with experimental observations. Both a large effective g factor for the ground state and a large temperature-independent part of the magnetic susceptibility arise because of a strong orbital contribution to the magnetic behavior of the Co(II) dimer.