The technique Fractional Order Model Reference Adaptive Control (FOMRAC) applied to an Automatic Voltage Regulator (AVR) is presented in this paper. The work is focused on tuning the adaptive gains and the derivation order of the adaptive laws of the FOMRAC, determined through the minimization of a criterion function defined for the simplified model of the AVR, by means of the genetic algorithm (GA) optimization technique. Based on the criterion function proposed by other authors a simulated comparative study is performed, comparing the proposed methodology with the integer order PID control reported in (Zamani et al., 2009). It is shown that the FOMRAC with parameters optimized by GA provides better results in terms of robustness under parameters variations of the system under control and improvements in the convergence speed of the control error.