In the context of a collaboration between the Medical University of Vienna, the Power Electronic Systems Laboratory of ETH Zurich, and Charité Berlin, the novel implantable total artificial heart (TAH) ShuttlePump is currently being developed. Its novel, low-complexity pumping concept requires a compact Linear-Rotary Actuator (LiRA). The Linear Actuator (LA) part was designed, realized, and experimentally verified in previous work, and it can provide a peak axial force of about 45 N with about 8 W of continuous power dissipation. This paper presents the details of the Rotary Actuator (RA) part. This has considerably lower output power requirements (about 100 mW) due to the low operating torque and angular speed (3.1 mNm and up to 300 rpm, respectively). However, the RA is highly constrained spatially, as it needs to be integrated very close to the previously realized LA. This forces a permanent magnet synchronous machine (PMSM) design with a rotor only partially equipped with PMs and stators covering only half of the total circumference, which introduces a considerable cogging component to the total torque. The proposed PMSM is hence optimized using Finite Element Methods (FEM) simulations to select a final design with low power losses and low cogging-induced angular speed ripple. The machine is realized as a hardware prototype, and the experimental measurements confirm that the proposed RA can meet the continuous torque requirement with 324 mW of power losses. The successful implementation of the RA (and LA) finally verifies the practical feasibility of the integrated LiRA and provides the basis for a comprehensive test of the complete ShuttlePump in a hydraulic test rig in the course of further research.