An electric current controlled spin-wave logic gate based on a width-modulated dynamic magnonic crystal is realized. The device utilizes a spin-wave waveguide fabricated from a single-crystal Yttrium Iron Garnet film and two conducting wires attached to the film surface. Application of electric currents to the wires provides a means for dynamic control of the effective geometry of the waveguide and results in a suppression of the magnonic band gap. The performance of the magnonic crystal as an AND logic gate is demonstrated.