Aerial Manipulator Systems (AMS) have garnered significant interest for their utility in aerial operations. Nonetheless, challenges related to the manipulator's limited stiffness and the coupling disturbance with manipulator movement persist. This paper introduces the Aerial Tendon-Driven Manipulator (ATDM), an innovative AMS that integrates a hexrotor Unmanned Aerial Vehicle (UAV) with a 4-degree-of-freedom (4-DOF) anthropomorphic tendon-driven manipulator. The design of the manipulator is anatomically inspired, emulating the human arm anatomy from the shoulder joint downward. To enhance the structural integrity and performance, finite element topology optimization and lattice optimization are employed on the links to replicate the radially graded structure characteristic of bone, this approach effectively reduces weight and inertia while simultaneously maximizing stiffness. A novel tensioning mechanism with adjustable tension is introduced to address cable relaxation, and a Tension-amplification tendon mechanism is implemented to increase the manipulator's overall stiffness and output. The paper presents a kinematic model based on virtual coupled joints, a comprehensive workspace analysis, and detailed calculations of output torques and stiffness for individual arm joints. The prototype arm has a total weight of 2.7 kg, with the end effector contributing only 0.818 kg. By positioning all actuators at the base, coupling disturbance are minimized. The paper includes a detailed mechanical design and validates the system's performance through semi-physical multi-body dynamics simulations, confirming the efficacy of the proposed design.