This paper investigates a practical precoding scheme for rate-splitting multiple access (RSMA) in multi-user multiple-input single-output (MU-MISO) systems where the nonlinear characteristics of power amplifiers are explicitly taken into account. To enhance performance in the presence of distortion caused by nonlinear power amplifiers, we propose an iterative accelerated gradient-based precoding scheme. The proposed precoding scheme is further integrated with a novel power scaling function that dynamically adjusts transmit power to satisfy practical power consumption constraints while maximizing an achievable sum rate. The gradient of the achievable sum rate for the considered system is derived to support efficient gradient-based optimization. We also prove that the proposed iterative precoding scheme converges to a critical point. Simulation results demonstrate that the proposed precoding scheme consistently outperforms modified conventional schemes including distortion-aware and weighted minimum mean square error beamforming, across both overloaded and underloaded scenarios. In particular, the proposed scheme demonstrates consistent performance in high-power regimes, where conventional schemes exhibit severe degradation due to distortion. Furthermore, the proposed precoding scheme exhibits faster convergence compared to the conventional benchmark.