The electron paramagnetic resonance spectra of impurity trivalent erbium ions in synthetic forsterite single crystals (Mg_2SiO_4) have been studied by the electron paramagnetic resonance method in the X and Q frequency bands. It is found that erbium ions predominantly substitute for magnesium ions in crystallographic position M1 that is characterized by the inversion symmetry of the crystal field. In this case, a pronounced effect of dimer self-organization of erbium ions during the crystal growth takes place; the effect is manifested in the fact that the concentration of erbium dimer associates consisting of two closely spaced ions bound by the spin– spin interaction is several orders of magnitude higher than the concentration of dimer associates that form randomly at a statistical distribution of impurity ions in the forsterite crystal lattice. The directions of the main magnetic axes and the parameters of the effective spin Hamiltonian describing the magnetic characteristics of impurity erbium centers have been determined.