We present a phase-shifting digital holographic microscopy technique, where a digital micromirror device enables to perform a precise phase-only shift of the reference wave. By coupling the beam into a monomode fiber, we obtain a laser mode with a constant phase shift, equally acting on all pixels of the hologram. This method has the advantage of being relatively simple and compatible with high frame rate cameras, which makes it of great interest for the observation of fast phenomena. We demonstrate the validity of the technique in an off-axis configuration by imaging living paramecia caudata.