The potential energy curves of the ground and twelve low-lying excited electronic states of the RbYb molecule have been calculated using the multi-reference perturbation theory method at the CASSCF/ XMCQDPT2 level of theory including the spin-orbit coupling. The electronic term energies, equilibrium internuclear distances, dissociation energies, transition dipole moments, the sequences of vibrational energies, the harmonic vibrational frequencies, and the Franck-Condon factors have been predicted. The potential energy curves at the asymptotic limits are in a good agreement with the experimental data for rubidium and ytterbium atoms. The obtained data would be useful for spectral experiments with RbYb molecules.