Physics-based simulations have accelerated the progress in learning-based across robotics, driving, manipulation, and locomotion. Yet, a fast, accurate, and robust surgical simulation environment remains a challenge. In this paper, we present ORBIT-Surgical, a physics-based surgical robot simulation framework with photorealistic rendering for the da Vinci Research Kit (dVRK) surgical robot. We provide twelve surgical tasks for the dVRK which represent common tasks in surgical training. ORBIT-Surgical leverages GPU parallelization to train reinforcement learning (RL) and imitation learning (IL) algorithms to facilitate study of robot learning for long-horizon surgical robotics tasks. ORBIT-Surgical also facilitates hand-scripted and human-expert realistic synthetic data collection for active perception tasks. We demonstrate ORBIT-Surgical sim-to-real transfer of learned policies to a physical dVRK robot.