Radiatively inefficient accretion flow models have been shown to accurately account for the spectrum and luminosity observed from Sgr A* in the X-ray regime down to mm wavelengths. However, observations at a few GHz cannot be explained by thermal electrons alone but require the presence of an additional non-thermal particle population. Here, we propose a model for the origin of such a population in the accretion flow via means of a pulsar orbiting the supermassive black hole in our Galaxy. Interactions between the relativistic pulsar wind with the disc lead to the formation of a bow shock in the wind. During the pulsar's transit through the accretion disc, relativistic pairs, accelerated at the shock front, are injected into the disc. The radio-emitting particles are long lived and remain within the disc long after the pulsar's transit. Periodic pulsar transits through the disc result in regular injection episodes of non-thermal particles. We show that for a pulsar with spin-down luminosity Lsd ∼ 3 × 1035 erg s-1 and a wind Lorentz factor of γw ∼ 104 a quasi-steady synchrotron emission is established with luminosities in the 1-10 GHz range comparable to the observed one.