[en] Full text.By taking into consideration the spin-orbit effect, the potential energy has been calculated over a wide range of internuclear distance for numerous electronic states of symmetry ²□⁺, ²□, ²□ and Ω of the molecular ion RbCs+ and by using the package CIPSI (Configuration Interaction by Perturbation of multiconfiguration wave function Selected Iterative) of Laboratoire de Physique Quantique (Toulouse-France). This calculation is done by using an ab initio method based on non-empirical pseudopotentials, parameterized l-dependent polarization potentials. Molecular orbitals for the molecular ion RbCs+ were derived from Self Consistent Field calculations (SCF), and full valence Configuration Interaction (CI) calculations were performed. A rovibrational study is done by calculating the eigenvalues E_v, the rotational constant B_v, teh centrifugal distortion constant D_v (up to 120 vibrational levels) and the spectroscopic constants for four bound states ²Λ⁺ and Ω. To the best of our knowledge, neither theoretical noe experimental data are available in the literature for the molecular ion RbCs+. Extensive tables of energy values versus internuclear distance are displayed at the following address http:lasim.univ-lyon1.fr/allouche/mcs.htm