Context. After the so-called cosmic recombination, the expanding universe entered into a period of darkness since most of the matter was in a neutral state. About a billion years later, however, the intergalactic space was once again ionized. The process, known as the cosmic reionization, required the operation of mechanisms that are not well understood. Among other ionizing sources, Population III stars, mini-quasars, and X-ray emitting microquasars have been invoked. Aims. We propose that primordial cosmic rays, accelerated at the termination points of the jets of the first microquasars, may have contributed to the reionization of the intergalactic space as well. Methods. We quantify the ionization power of cosmic rays (electrons and protons) in the primordial intergalactic medium. This power is calculated using extensive particle cascade simulations. Results. We establish that, depending on the fraction of electrons to protons accelerated in the microquasar jets, cosmic rays should have contributed to the reionization of the primordial intergalactic medium as much as X-rays from microquasar accretion disks. If the primordial magnetic field was of the order of 10-17 G, as some models suggest, cosmic rays had an important role in ionizing the neutral material far beyond the birth places of the first stars.Facultad de Ciencias Astronómicas y Geofísicas