A 220 diamond phase plate was combined with an energy-dispersive absorption spectrometer to convert linearly polarized X-rays into circularly polarized photons and to detect circular magnetic X-ray dichroism (CMXD) from ferromagnetic samples. In these experiments, carried out at LURE, the energy-dispersive spectrometer was equipped with a bent Si (311) polychromator and vertically collimating slits accepting essentially a linearly polarized incident beam. The quarter-wave plate was operated in the Bragg geometry but well outside the range of quasi total reflection, with the consequence that the forward-diffracted beam was circularly polarized with a polarization rate approaching 80% over the whole energy bandpass of the polychromator. CMXD spectra of GdFe2 and GdCo2 intermetallic compounds were recorded at ca 7.2 keV near the Gd LIII absorption edge: they are essentially identical to the spectra commonly recorded with elliptically polarized X-ray photons collected out of the orbit plane of the storage ring. It is suggested that the energy-dispersive phase plate will be very useful to detect CMXD spectra with energy-dispersive spectrometers exploiting the well collimated linearly polarized emission of standard undulators installed on the storage rings of the third generation.