Photoionization process is a subject of special importance in many areas of physics. Numerical methods must be used in order to obtain photoionization cross-sections for non-hydrogenic levels. The atomic data required to calculate them is huge and self-consistent calculations increase computing time considerably, overall when we are studying plasmas where it is found million of ion levels. Analytical potentials are a useful alternative because they avoid the iterative procedures typical in self-consistent models. In this work, we present a relativistic quantum-mechanic calculation of photoionization cross-sections for non-hydrogenic ions immersed in weakly coupled plasmas. Both the energy levels and bound and free wave functions are determined by means of the Dirac equation. It is employed as effective potential an analytical one developed to model non-isolated many-electron ions making use of the Debye-Hu¨ckel approach but including the reaction of the plasma-charge density to the optical electron. The effect of the plasma screening in the photoionization cross-section and in the threshold energy is analyzed as a function of the photon energy, the Debye radius, the ionization and the monoelectronic bound level involved in the transition. Some comparisons between our results and others are also made.