Computer graphics is generally divided into two branches: real-time rendering and physically-based rendering. Conventional graphics processing units (GPUs) were designed to accelerate the former which is based on the standard Z-buffer algorithm. However, many applications in entertainment, science, and industry require high quality visual effects such as soft-shadows, reflections, and diffuse lighting interactions which are difficult to achieve with the Z-buffer algorithm, but are straightforward to implement using physically-based rendering methods. Physically-based rendering can already be implemented on present programmable GPUs. However, for physically-based rendering on GPUs, a large portion of the processing power is wasted due to low utilization of SIMD units. This is because the core algorithm of physically-based rendering, ray tracing, suffers from Single Instruction, Multiple Thread (SIMT) control flow divergences. In this paper, we propose the Dynamic Ray Shuffling (DRS) architecture for GPUs to address this problem. Our key insight is that the primary control flow divergences are caused by inconsistent ray traversal states of a warp, and can be eliminated by dynamically shuffling rays. Experimental results show that, for an estimated 0.11% area cost, DRS significantly improves the SIMD efficiency for the tested benchmarks from 41.06% to 81.04% on average. With this, the performance of a physically-based rendering method such as path tracing can be improved by 1.67X--1.92X, and 1.79X on average.