To address the output-current fluctuation, transfer-efficiency degradation, and stability deterioration caused by coupler misalignment in magnetically coupled wireless power transfer (MC-WPT) systems, this paper proposes a misalignment-tolerant method for a dual-sided LCC-compensated WPT system based on switch-controlled capacitor (SCC) regulation. This system employs an X-shaped ring-periphery composite transmitter coil and a circular receiver coil (XRPC-CR). First, the XRPC-CR-based dual-sided LCC topology is established, and its operating modes, resonant conditions, and transfer characteristics are analyzed. A mathematical model relating the output current to the key system parameters is then derived. Second, the misalignment characteristics of the system under different offset conditions are investigated, and the underlying SCC-enabled misalignment-tolerant mechanism is revealed. On this basis, a DSP-based dual-channel SCC control strategy is developed to achieve constant-current output under misaligned conditions by adjusting the tuning coefficients. Subsequently, an MWorks simulation model is built to evaluate the output current and transfer efficiency under three representative scenarios, namely receiver self-rotation, horizontal and vertical misalignment, and receiver revolution around the transmitter coil. The results show that the proposed method maintains favorable output stability under multiple misalignment conditions, with system error constrained within 2.5% and the transfer efficiency remaining above 75.0%, demonstrating strong misalignment-tolerant regulation capability. Finally, an experimental platform is established to validate the proposed method. Experimental results demonstrate that stable current output can still be achieved when the receiver-coil offset is within one-quarter of the coil dimension, with the error as low as 2.5% and the transfer efficiency reaching up to 89.50%. The close agreement between simulation and experimental results verifies the effectiveness of the proposed method in improving both misalignment tolerance and overall system performance, thereby indicating its practical engineering value.