To investigate the impact of crack inclination angle on the tensile strength and characteristics of splitting failure in rock, split tests were conducted on fine-grained sandstone with pre-existing cracks under different crack inclination angle conditions. Acoustic emission and digital image techniques were continuously monitored during the tests. The evolution of absorbed energy during the loading and failure processes was calculated and discussed, aiming to elucidate the interconnections among the maximum absorbed energy, the pre-existing crack inclination angle, the tensile strength, and the acoustic emission energy of the rock, which can provide a reference for the design and construction of tunnels or mines in rock formations with pre-existing cracks. The experimental findings indicate the following: (1) The tensile strength and failure displacement decrease first and then increase with the increase in the pre-existing crack inclination angle, demonstrating an approximate “V”-shaped alteration. (2) The failure modes of specimens with pre-existing cracks can be classified into three types: tensile failure along the center of the disk, tensile failure along the tip of the pre-existing crack, and tensile–shear composite failure along the tip of the pre-existing crack. (3) The crack inclination angle exerts a substantial influence on the evolution curve of energy absorption. The maximum energy absorption of the specimens first increases and then decreases with the increase in the crack inclination angle. Moreover, a corresponding nonlinear relationship is observed between the maximum energy absorption and the tensile strength, as well as the AE energy.