This work presents a comprehensive numerical study for designing a lead-free, all-inorganic, and high-performance solar cell based on Cs2TiI6 halide perovskite with all-inorganic carrier transport layers. A rigorous ab initio density-functional theory (DFT) calculation is performed to identify the electronic and optical properties of Cs2TiI6 and, upon extraction of the existing experimental data of the material, the cell is designed and optimized to the degree of practical feasibility. Consequently, a theoretical power conversion efficiency (PCE) of 21.17% is reported with inorganic TiO2 and CuI as carrier transport layers. The calculated absorption coefficient of Cs2TiI6 reveals its enormous potential as an alternative low-bandgap material for different solar cell applications. Furthermore, the role of different point defects and the corresponding defect densities on cell performance are investigated. It is found that the possible point defects in Cs2TiI6 can form both the shallow and deep defect states, with deep defect states having a prominent effect on cell performance. For both defect states, the cell performance deteriorates significantly as the defect density increases, which signifies the importance of high-quality material processing for the success of Cs2TiI6-based perovskite solar cell technology.