The electronic and thermal transport properties of the Earth's core are crucial for many geophysical models such as the geodynamo model of the Earth's magnetic field. We show by first-principles modeling and methods of statistical physics that the spin disorder, not considered in previous studies, gives an essential contribution to the electrical resistivity at the Earth's core conditions. The origin of this spin-disorder resistivity (SDR) consists in the existence of fluctuating local moments that are stabilized at high temperatures by the magnetic entropy even at pressures at which the ground state of iron is non-magnetic. It turns out that the contributions of various scattering mechanisms (alloy disorder, phonon scattering, spin disorder, and electron-electron correlations) are comparable, but not additive. Here we report results for iron and iron-rich alloys (Fe-O, Fe-Si, Fe-S) that can be present in the Earth's core. Special attention is paid to alloys with two magnetic elements (Fe-Ni).