The advent of tactile sensors in robotics has sparked many ideas on how robots can leverage direct contact measurements of their environment interactions to improve manipulation tasks.An important line of research in this regard is that of grasp force control, which aims to manipulate objects safely by limiting the amount of force exerted on the object.While prior works have either hand-modeled their force controllers, employed model-based approaches or have not shown sim-to-real transfer, we propose a model-free deep reinforcement learning approach that is trained in simulation and then transferred to the robot without further fine-tuning.We therefore present a simulation environment that produces realistic normal forces, which we use to train continuous force control policies.An evaluation in which we compare against a baseline and perform an ablation study shows that our approach outperforms the hand-modeled baseline, and that our proposed inductive bias and domain randomization facilitate sim-to-real transfer.