Proteins containing voltage-sensing domains (VSDs) translate changes in membrane potential into changes in ion permeability or enzymatic activity1-3. In channels, voltage change triggers a switch in conformation of the VSD, which drives gating in a separate pore domain, or, in channels lacking a pore domain, directly gates an ion pathway within the VSD4,5. Neither mechanism is well understood6. In the Shaker potassium channel, mutation of the first arginine residue of the S4 helix to a smaller uncharged residue makes the VSD permeable to ions ('omega current') in the resting conformation ('S4 down')7. Here we perform a structure-guided perturbation analysis of the omega conductance to map its VSD permeation pathway. We find that there are four omega pores per channel, which is consistent with one conduction path per VSD. Permeating ions from the extracellular medium enter the VSD at its peripheral junction with the pore domain, and then plunge into the core of the VSD in a curved conduction pathway. Our results provide a model of the resting conformation of the VSD.