In this study, a new method is presented for the realisation of the fractional order integrator. First, integer order approximate methods are analysed, then based on this analysis and using existing successfully applied approximate methods given in the literature, the design of fractional order integrators with active circuit elements is studied. In other words, fractance elements are developed. Operational amplifier is preferred in the design of fractional order integrator. Time responses of fractional order integrator circuits are computed by using Multisim software of National Instruments. Then the results are compared and verified with the results obtained from Matlab.