The ideas of topology have found tremendous success in closed physical systems, but even richer properties exist in the more general open or dissipative framework. We theoretically propose and experimentally demonstrate a bulk Fermi arc that develops from non-Hermitian radiative losses in an open system of photonic crystal slabs. Moreover, we discover half-integer topological charges in the polarization of far-field radiation around the bulk Fermi arc. Both phenomena are shown to be direct consequences of the non-Hermitian topological properties of exceptional points, where resonances coincide in their frequencies and linewidths. Our work connects the fields of topological photonics, non-Hermitian physics and singular optics, providing a framework to explore more complex non-Hermitian topological systems.