When a charged particle translates through an electrolyte solution, the electric double layer around it deforms in response to the fluid motion and creates an electric force opposite the direction of motion, decreasing the settling velocity. This is a multidisciplinary phenomenon that combines fluid mechanics and electrodynamics, differentiating it from the classical problem of an uncharged sedimenting particle. It has many applications varying from mechanical to biomedical, such as in drug delivery in blood through charged microparticles. Related studies so far have focused on Newtonian fluids, but recent studies have proven that many biofluids, such as human blood plasma, have elastic properties. To this end, we perform a computational study of the steady sedimentation of a spherical, charged particle in human blood plasma due to the centrifugal force. We used the Giesekus model to describe the rheological behavior of human blood plasma. Assuming axial symmetry, the governing equations include the momentum and mass balances, Poisson's equation for the electric field, and the species conservation. The finite size of the ions is considered through the local-density approximation approach of Carnahan-Starling. We perform a detailed parametric analysis, varying parameters such as the ζ potential, the size of the ions, and the centrifugal force exerted upon the particle. We observe that as the ζ potential increases, the settling velocity decreases due to a stronger electric force that slows the particle. We also conduct a parametric analysis of the relaxation time of the material to investigate what happens generally in viscoelastic electrolyte solutions and not only in human blood plasma. We conclude that elasticity plays a crucial role and should not be excluded from the study. Finally, we examine under which conditions the assumption of point-like ions gives different predictions from the Carnahan-Starling approach.