Context. Impacts of dust grains on spacecraft are known to produce typical impulsive signals in the voltage waveform recorded at the terminals of electric antennas. Such signals (as may be expected) are routinely detected by the Time Domain Sampler (TDS) system of the Radio and Plasma Waves (RPW) instrument on board Solar Orbiter. Aims. We investigate the capabilities of RPW in terms of interplanetary dust studies and present the first analysis of dust impacts recorded by this instrument. Our purpose is to characterize the dust population observed in terms of size, flux, and velocity. Methods. We briefly discuss previously developed models of voltage pulse generation after a dust impact onto a spacecraft and present the relevant technical parameters for Solar Orbiter RPW as a dust detector. Then we present the statistical analysis of the dust impacts recorded by RPW/TDS from April 20, 2020 to February 27, 2021 between 0.5 AU and 1 AU. Results. The study of the dust impact rate along Solar Orbiter’s orbit shows that the dust population studied presents a radial velocity component directed outward from the Sun. Its order of magnitude can be roughly estimated as v_{r, dust} ≃ 50 km s⁻¹, which is consistent with the flux of impactors being dominated by β-meteoroids. We estimate the cumulative flux of these grains at 1 AU to be roughly F_β ≃ 8 × 10⁻⁵ m⁻² s⁻¹ for particles of a radius r ≳ 100 nm. The power law index δ of the cumulative mass flux of the impactors is evaluated by two differents methods, namely: direct observations of voltage pulses and indirect effect on the impact rate dependency on the impact speed. Both methods give the following result: δ ≃ 0.3 − 0.4. Conclusions. Solar Orbiter RPW proves to be a suitable instrument for interplanetary dust studies, and the dust detection algorithm implemented in the TDS subsystem an efficient tool for fluxes estimation. These first results are promising for the continuation of the mission, in particular, for the in situ study of the inner Solar System dust cloud outside of the ecliptic plane, which Solar Orbiter will be the first spacecraft to explore.