Calculations have been carried out for C4H4X2 cyclic molecules, with X=O, S, Se, and Te, characterized by the presence of magnetic-field induced toroidal electron currents and associated orbital anapole moments. The orbital anapole induced by a static nonuniform magnetic field B, with uniform curl C=∇×B, is rationalized via a second-rank anapole magnetizability tensor a(αβ), defined as minus the second derivative of the second-order interaction energy with respect to the components C(α) and B(β). The average anapole magnetizability a̅ equals -χ̅, the pseudoscalar obtained by spatial averaging of the dipole-quadrupole magnetizability χ(α,βγ). It has different sign for D and L enantiomeric systems and can therefore be used for chiral discrimination. Therefore, in an isotropic chiral medium, a homogeneous magnetic field induces an electronic anapole A(α), having the same magnitude, but opposite sign, for two enantiomorphs.