The development of robotic grippers and hands for automation aims to emulate human dexterity without sacrificing the efficiency of industrial grippers. This study introduces Rotograb, a tendon-actuated robotic hand featuring a novel rotating thumb. The aim is to combine the dexterity of human hands with the efficiency of industrial grippers. The rotating thumb enlarges the workspace and allows in-hand manipulation. A novel joint design minimizes movement interference and simplifies kinematics, using a cutout for tendon routing. We integrate teleoperation, using a depth camera for real-time tracking and autonomous manipulation powered by reinforcement learning with proximal policy optimization. Experimental evaluations demonstrate that Rotograb's rotating thumb greatly improves both operational versatility and workspace. It can handle various grasping and manipulation tasks with objects from the YCB dataset, with particularly good results when rotating objects within its grasp. Rotograb represents a notable step towards bridging the capability gap between human hands and industrial grippers. The tendon-routing and thumb-rotating mechanisms allow for a new level of control and dexterity. Integrating teleoperation and autonomous learning underscores Rotograb's adaptability and sophistication, promising substantial advancements in both robotics research and practical applications.