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Shape Memory Alloy (SMA) wires are currently employed in robotics as actuators of prosthetic limbs and medical equipment due to advantages such as reducing the size in the application, high power-to-weight ratio and elimination of complex transmission systems. In this paper, a fuzzy control system has been designed and implemented for an artificial finger using the SMA actuators. This robotic finger has been designed and modeled with three revolute joints and three SMA wires as the tendon in order to adduction each phalange of the finger and torsional springs to restore them to their original positions. The dynamic model of the finger has been simulated in MATLAB/Simulation. Based on the simulation results, optimal choice of parameters and system features has been obtained and a prototype of finger has been built and tested. Gains of the controllers are set so that the current applied to SMA wires has minimum overshoot and the output of the system has minimal time to achieve stability. The comparison between the simulation results and the actual measured data show that the simulated model is accurate.