The rock-socketed pier anchored by inclined anchors (RPIA) is a new type of foundation developed by combining a rock-socketed pier and inclined anchors. Current research on RPIA is relatively limited, and the impact of design parameters on its bearing performance remains unclear. To investigate the uplift-bearing performance of RPIA, a finite-element model that considers the nonlinear properties of materials and multidirectional interactions was developed and verified. Based on this model, numerical simulations were performed on twenty-five RPIA that were designed using the L25 orthogonal array proposed by the Taguchi method, and the uplift load–displacement curve for each RPIA was obtained. Based on the interpretation of the elastic limit, uplift resistance, initial stiffness, and the ductility index for each simulated RPIA, the sensitivity of each factor was examined by analyzing the signal-to-noise ratio and variance. The results indicated that rock strength and pier diameter were the main factors determining the uplift performance of the RPIAs, while the angle of inclined anchors is the most influential factor affecting the ductility of RPIA. The primary role of the inclined anchor is to reduce the extraction of the pier after failure of the side resistance between the pier and rock mass, thus significantly enhancing the ductility of the uplift-loaded RPIA. The addition of reinforcements around the connection joints of the pier and anchors may prevent concrete failure and to fully execute the role of inclined anchors.