Higgsinos with masses near the electroweak scale can solve the hierarchy problem and provide a dark matter candidate, while detecting them at the LHC remains challenging if their mass splitting is O(1  GeV). This Letter presents a novel search for nearly mass-degenerate Higgsinos in events with an energetic jet, missing transverse momentum, and a low-momentum track with a significant transverse impact parameter using 140  fb^{-1} of proton-proton collision data at sqrt[s]=13  TeV collected by the ATLAS experiment. For the first time since LEP, a range of mass splittings between the lightest charged and neutral Higgsinos from 0.3 to 0.9 GeV is excluded at 95% confidence level, with a maximum reach of approximately 170 GeV in the Higgsino mass.