We demonstrate a novel way of synthesizing spin-orbit interactions in ultracold quantum gases, based on a single-photon optical clock transition coupling two long-lived electronic states of two-electron 173Yb atoms. By mapping the electronic states onto effective sites along a synthetic ``electronic{''} dimension, we have engineered fermionic ladders with synthetic magnetic flux in an experimental configuration that has allowed us to achieve uniform fluxes on a lattice with minimal requirements and unprecedented tunability. We have detected the spin-orbit coupling with fiber-link-enhanced clock spectroscopy and directly measured the emergence of chiral edge currents, probing them as a function of the flux. These results open new directions for the investigation of topological states of matter with ultracold atomic gases.