Fractional calculus techniques (non-integer order systems) have been successfully applied in many fields of electronics and engineering. In this paper the effects of including fractional order electronic components on the radiated antenna pattern of a circular loop antenna is presented. A fractional order “RLC” impedance matching circuit is placed between the generator and the equivalent circuit of a loop antenna. The input impedance of the antenna and the antenna gain are controllable through varying the fractional orders of an inductive element and a capacitive element (Fractors) in the matching network. The circuit is presented and solved analytically, and some numerical simulations follow. We discuss the effects of fractional order components on the resulting radiation patterns. In particular, the amplitude of the antenna gain is controlled by the fractional order parameters. This effect could be exploited in future for antenna beam-forming applications when using an array of antenna elements. Further, the input impedance of the antenna circuit can also be controlled by the fractional order components. The introduction of fractional order variables provides for higher degrees of freedom, enabling a flexible approach to tuning antennas for optimal performance.