The present invention relates to the production of reflectarray antennas, that is to say antennas consisting of a primary illumination source and a phase-shifting plate consisting of an array of cells each having a coefficient of reflection the phase of which is electronically controlled. According to the invention, each cell consists of a waveguide element closed at one of its ends by a dielectric substrate wafer carrying an electrical circuit formed by three parallel conducting strips. A variable capacitor, produced either in MEMS technology or by means of a ferroelectric element, is implanted by means of bonding wires on the electrical circuit etched on the substrate. The shape and the arrangement of the three parallel conducting strips constituting the electrical circuit and the way in which the variable capacitor is connected to this circuit make it possible to form, in the plane of the substrate, a phase shifter circuit, the phase shift of which may vary almost continuously over a wide range of variation. Advantageously, the phase shifter circuit thus formed occupies a small volume. The invention applies to the production of dual-polarization reflectarray antennas.