The development of stable, non-toxic, and high-efficiency perovskite materials is critical for advancing next-generation photovoltaic technologies. While numerous halide double perovskites have been explored, many suffer from indirect band gaps or limited optoelectronic tunability. In this work, we employ first principles calculations to investigate the structural, electronic, and optical characteristics of the rubidium-based double perovskite Rb₂NaTlBr₆. Our results reveal that the compound exhibits a direct band gap of 1.869 eV, along with strong, dynamic and thermodynamic stability. Notably, the application of tensile strain engineering systematically reduces the band gap to 1.374 eV, placing it within the optimal range for solar absorption and significantly enhancing its optoelectronic response. The material also demonstrates high absorption coefficients and favorable carrier effective masses. Importantly, the spectroscopic limited maximum efficiency (SLME) reaches 33% under 5% tensile strain, underscoring its photovoltaic potential. The findings suggest that strain engineered Rb₂NaTlBr₆ is promising, lead-free candidate for high-efficiency solar energy applications.