A prototype tile current array, consisting of resistors to sense current flowing from six divertor tiles into the metallic vacuum vessel, was installed in DIII-D. Data show that typically 1-2 kA circulates poloidally around the single-null divertor scrapeoff layer (SOL). A current of similar magnitude flows vertically in the outer SOL of double-null plasmas and a much smaller current in the inner SOL. Little or no current flows across the short SOL connecting the inner and outer divertor strike points. The SOL current increases with core plasma current and edge localized modes (ELMs); it decreases at the onset of the H-mode and with heavy gas puffing. The SOL current jumps rapidly to 5-10 kA during giant ELM events. Three possible mechanisms to drive the SOL current are examined qualitatively with respect to the data, but the evidence is insufficient to identify the dominant one. During disruptions, poloidal current in excess of 100 kA flows to the wall.