The pressure evolution of the magnetic properties of the Ce2RhIn7.79Cd0.21 heavy fermion compound was investigated by single crystal neutron magnetic diffraction and electrical resistivity experiments under applied pressure. From the neutron magnetic diffraction data, up to P = 0.6 GPa, we found no changes in the magnetic structure or in the ordering temperature TN = 4.8 K. However, the increase of pressure induces an interesting spin rotation of the ordered antiferromagnetic moment of Ce2RhIn7.79Cd0.21 into the ab tetragonal plane. From the electrical resistivity measurements under pressure, we have mapped the evolution of TN and the maximum of the temperature dependent electrical resistivity (TMAX) as a function of the pressure (P ≲ 3.6 GPa). To gain some insight into the microscopic origin of the observed spin rotation as a function of pressure, we have also analyzed some macroscopic magnetic susceptibility data at ambient pressure for pure and Cd-doped Ce2RhIn8 using a mean-field model including tetragonal crystalline electric field (CEF). The analysis indicates that these compounds have a Kramers doublet Γ7- -type ground state, followed by a Γ7+ first excited state at Δ1 ∼ 80 K and a Γ6 second excited state at Δ2 ∼ 270 K for Ce2RhIn8 and Δ2 ∼ 250 K for Ce2RhIn7.79Cd0.21. The evolution of the magnetic properties of Ce2RhIn8 as a function of Cd doping and the rotation of the direction of the ordered moment for the Ce2RhIn7.79Cd0.21 compound under pressure suggest important changes of the single ion anisotropy of Ce3+ induced by applying pressure and Cd doping in these systems. These changes are reflected in modifications in the CEF scheme that will ultimately affect the actual ground state of these compounds.