<p>This study explores the self-focusing behavior of a linearly polarized laser beam as it propagates through a semi-bounded weakly relativistic magnetized thermal quantum plasma. The dynamics of the plasma are described using the quantum hydrodynamic (QHD) model, which accounts for quantum effects such as electron degeneracy pressure, originating from Fermi statistics and the Bohm potential, which arises due to quantum tunneling, along with relativistic modifications. An external magnetic field is applied in the direction of laser propagation. When the laser enters the plasma, the presence of the magnetic field causes its linear polarization to split it to right and left circularly polarized components. This change in polarization, significantly affects the dynamics of the plasma particles. To derive the nonlinear wave equation for the circularly polarized laser beam in quantum weakly relativistic magnetized thermal plasma, a perturbative method is employed. The equation result clearly reveals how quantum and relativistic effects influence the plasma’s dispersion relation and its effective refractive index. Finally, a set of coupled equations is obtained for the self-focusing behavior of the right- and left-handed modes that emerge from the initially linearly polarized laser beam. The analysis shows that quantum effects, such as the quantum potential and Fermi pressure, alter the beam’s behavior and influence its self-focusing. Increasing the magnetic field strength enhances the self-focusing, while increasing the laser frequency tends to weaken it. Moreover, an increase in plasma density and laser intensity further enhances the self-focusing of the beam.</p>