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 are routinely detected by the Time Domain Sampler (TDS) system of the Radio and Plasma Waves (RPW) instrument aboard Solar Orbiter. We investigate the capabilities of RPW in terms of interplanetary dust studies and present the first analysis of dust impacts recorded by this instrument. We discuss previously developed models of voltage pulses 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 20th, 2020 to February 27th, 2021 between 0.5 AU and 1 AU. The study shows that the dust population studied presents a radial velocity component directed outward from the Sun, the order of magnitude of which can be roughly estimated as $v_{r, dust} simeq 50$ km.$s^{-1}$. This is consistent with the flux of impactors being dominated by $beta$-meteoroids. We estimate the cumulative flux of these grains at 1 AU to be roughly $F_beta simeq 8times 10^{-5} $ m$^{-2}$s$^{-1}$, for particles of radius $r gtrsim 100$ nm. The power law index $delta$ of the cumulative mass flux of the impactors is evaluated by two differents methods (direct observations of voltage pulses and indirect effect on the impact rate dependency on the impact speed). Both methods give a result $delta simeq 0.3-0.4$. Solar Orbiter RPW proves to be a suitable instrument for interplanetary dust studies. These first results are promising for the continuation of the mission, in particular for the in-situ study of the dust cloud outside the ecliptic plane, which Solar Orbiter will be the first spacecraft to explore.
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