Unmanned Aerial Vehicles (UAV)-based photogrammetry provides an efficient solution for shallow water bathymetry, yet its accuracy is fundamentally constrained by light refraction at the air-water interface, which violates the central geometric assumptions of traditional photogrammetry. Existing approaches, ranging from empirical corrections and iterative post-processing to black-box deep learning, often compromise geometric fidelity, physical interpretability, or generalization. We address this challenge through Refraction-Aware Gaussian Splatting (RA-GS), which embeds a physically rigorous two-media refraction model directly into the Gaussian Splatting (GS) reconstruction pipeline. Rather than relying on computationally expensive per-pixel ray tracing, we formulate an analytical parameter transformation that maps the true underwater position, scale, and opacity of each Gaussian to their apparent states observed through a planar refractive interface. Through this fully differentiable transformation, true underwater 3D geometry and photorealistic appearance are jointly optimized by directly minimizing the photometric error within the standard GS framework. This approach relies solely on RGB imagery, eliminating the need for external depth priors or deep learning networks. Using a physically based, ray-traced synthetic riverbed dataset, we isolate and explicitly correct refractive distortions. Our method achieves a geometric F1-score of 94% (10 cm threshold at 10 m depth) and produces high-quality novel view synthesis with a PSNR of 25.9 dB and SSIM of 0.93. Field experiments on real UAV data corroborate the practical utility for high-precision bathymetric mapping under calm-surface conditions. By resolving the fundamental refractive difficulty, the proposed framework provides a physically grounded, computationally efficient, and practically useful solution for next-generation photogrammetric bathymetry.