We introduce a novel and efficient method for rendering large models composed of individually-oriented voxels. The core of this method is a new algorithm for computing the intersection point and normal of a 3D ray with an arbitrarily-oriented 3D box, which also has non-rendering applications in GPU physics, such as ray casting and particle collision detection. We measured throughput improvements of 2× to 10× for the intersection operation versus previous ray-box intersection algorithms on GPUs. Applying this to primary rays increases throughput 20× for direct voxel ray tracing with our method versus rasterization of optimal meshes computed from voxels, due to the combined reduction in both computation and bandwidth. Because this method uses no precomputation or spatial data structure, it is suitable for fully dynamic scenes in which every voxel potentially changes every frame. These improvements can enable a dramatic increase in dynamism, view distance, and scene density for visualization applications and voxel games such as LEGO® Worlds and Minecraft. We provide GLSL code for both our algorithm and previous alternative optimized ray-box algorithms, and an Unreal Engine 4 modification for the entire rendering method.