Earth's solid inner core is surrounded by a convecting liquid outer core, creating the geodynamo driving the planet's magnetic field. Seismic studies using compressional body waves suggest hemispherical variation in the anisotropic structure of the inner core, but are poorly constrained because of limited earthquake and receiver distribution. Here, using normal mode splitting function measurements from large earthquakes, based on extended cross-coupling theory, we observe both regional variations and eastern versus western hemispherical anisotropy in the inner core. The similarity of this pattern with Earth's magnetic field suggests freezing-in of crystal alignment during solidification or texturing by Maxwell stress as origins of the anisotropy. These observations limit the amount of inner core super rotation, but would be consistent with oscillation.