The origins of the lunar crustal magnetic fields remain unclear although dozens of magnetic field measurements have been conducted on and above the lunar surface. A major obstacle to resolving this problem is the extreme difficulty of determining a surface distribution of small-scale magnetization. We present a new technique to map small-scale magnetic fields using nonadiabatic scattering of high-energy electrons in the terrestrial plasma sheet. Particle tracing, utilizing three-dimensional lunar magnetic field data synthesized from magnetometer measurements, enables us to separate the contributions to electron motion of small- and large-scale magnetic fields. We map significant kilometer-scale magnetic fields on the southwestern side of the South Pole-Aitken basin that are correlated with larger-scale magnetization. This implies that kilometer-scale magnetization may be ubiquitous over the lunar surface and related to the large-scale magnetization.