We have developed a parameter optimization tool, Monte Carlo Josephson simulator (MJSIM), for rapid single flux quantum (RSFQ) digital circuits based on a Monte Carlo yield analysis. MJSIM can generate a number of net lists for the JSIM, where all parameter values are varied randomly according to the Gaussian distribution function, and calculate the circuit yields automatically. MJSIM can also produce an improved parameter set using the algorithm of the center-of-gravity method. In this algorithm, an improved parameter vector is derived by calculating the average of parameter vectors inside and outside the operating region. As a case study, we have optimized the circuit parameters of an RS flip-flop, and investigated the validity and efficiency of this optimization method by considering the convergency and initial condition dependence of the final results. We also proposed a method for accelerating the optimization speed by increasing 3σ spreads of the parameter distribution during the optimization.