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We characterize asteroid (16) Psyche using high-precision astrometry, including the recent Gaia Focused Product Release. The gravitational perturbations of Psyche on other asteroids can be observable in the case of mutual encounters. Using a least squares approach, we estimate the mass of Psyche by fitting astrometric data of asteroids that come within 0.05 au of Psyche. Combining the resulting individual estimates, we find GM = 1.601 ± 0.017 km ^3 s ^−2 . This result is robust against variations in the orbit determination setup and specific data set used. The volume and equivalent radius of Psyche are currently constrained by occultations and radar and optical imaging to (5.75 ± 0.19) × 10 ^6 km ^3 and ${111}_{-0.5}^{+2}$ km, respectively. Given the volume of Psyche, our mass estimate corresponds to a bulk density of 4172 ± 145 kg m ^−3 , which is compatible with an M-type taxonomic classification. Finally, the phase-dependent photocenter offset is visible in the residuals of Gaia astrometric observations of Psyche. This effect is consistent with the size of Psyche.