Next-generation xenon detectors with multiton-year exposure are powerful direct probes of dark matter candidates, in particular the favorite weakly interacting massive particles. Coupled with the features of low thresholds and backgrounds, they are also excellent telescopes of solar neutrinos. In this paper, we study the discovery potential of ton-scale xenon detectors in electromagnetic moments of solar neutrinos. Relevant neutrino-atom scattering processes are calculated by applying a state-of-the-art atomic many-body method-relativistic random phase approximation. Limits on these moments are derived from existing data and estimated with future experiment specifications. With one ton-year exposure, XENON-1T can improve the effective millicharge constraint by a factor of 2. With LZ and DARWIN, the projected improvement on the solar neutrino effective millicharge (magnetic moment) is around 7 (2) times smaller than the current bound. If LZ can keep the same background level and push the electron recoil threshold to 0.5 keV, the projected improvement on the millicharge (magnetic moment) is about 10 (3) times smaller than the current bound. An unconventional setup of placing a strong 51Cr neutrino source by a ton-scale xenon detector is also considered.