Structured features on top of nominally smooth distributions of radiation-belt particles at Earth have been previously associated with particle acceleration and transport mechanisms powered exclusively by enhanced solar-wind activity. Although planetary rotation is considered to be important for particle acceleration at Jupiter and Saturn, the electric field produced in the inner magnetosphere by Earth's rotation can change the velocity of trapped particles by only about 1-2 kilometres per second, so rotation has been thought inconsequential for radiation-belt electrons with velocities of about 100,000 kilometres per second. Here we report that the distributions of energetic electrons across the entire spatial extent of Earth's inner radiation belt are organized in regular, highly structured and unexpected 'zebra stripes', even when the solar-wind activity is low. Modelling reveals that the patterns are produced by Earth's rotation. Radiation-belt electrons are trapped in Earth's dipole-like magnetic field, where they undergo slow longitudinal drift motion around the planet because of the gradient and curvature of the magnetic field. Earth's rotation induces global diurnal variations of magnetic and electric fields that resonantly interact with electrons whose drift period is close to 24 hours, modifying electron fluxes over a broad energy range into regular patterns composed of multiple stripes extending over the entire span of the inner radiation belt.