In this paper, we present Adaptive Neuro-Fuzzy Inference System (ANFIS)-based modelling and control of a compliant rotary actuator using Shape Memory Alloy (SMA) material. The SMA material has flexible behavior that can be suitable for compliant applications specially bio-inspired and soft robotics. The driving circuit used in this system is designed and implemented to be embedded in the same actuator. This embedded driving circuit provides compactness advantage for our proposed actuator to be effectively used in further applications with higher Degrees Of Freedom (DOF). The model of the SMA rotating actuator is obtained by system identification using ANFIS algorithm based on real experimental data. Closed-loop feedback control system is designed in the simulation based on the obtained ANFIS model. PID controller is ultimately implemented in the real system. The system response could attain a rise time of 0.5 sec and an overshoot of 8%. The controller could achieve satisfying tracking and disturbance rejection.