Spintronic is a new rising research field aiming to deal with both, the charge and the spin of electrons in order to process and store information. Spins in Heusler alloys offer a pathway toward the integration of information storage and processing in one single device. In this work, and among the less unreported compound, we present and discuss hydrostatic pressure effect on the electronic and magnetic properties of the CoRhMnSn Heusler alloy. The theoretical calculations were carried out using the pseudopotential plane-wave (PP-PW) method with the generalized gradient approximation (GGA-PBEsol). The geometric optimization of the CoRhMnSn crystalline structure was done for pressures ranging from -20 to 50 GPa. The calculated lattice parameter is consistent with both theoretical and experimental reports. The bulk modulus of the considered material is equal to 188 GPa, and therefore, this material has a relatively high resistance to volume changes. Electronic properties were determined by computing the electronic band structure of the titled compound. The obtained results show that the CoRhMnSn compound exhibits a nearly half-metallic (HM) character with a ferromagnetic state at 0GPa, and becomes a perfect HM at 35GPa. The hydrostatic pressure effect caused a significant variation of the spin polarization. The calculated total magnetic moment of CoRhMnSn is close to 5µB, in good agreement with the Slater-Pauling rule.