We demonstrate the use of a single trapped ion as a sensor to probe electric-field noise from interchangeable test surfaces. As proof of principle, we measure the magnitude and distance dependence of electric-field noise from two ion-trap-like samples with patterned Au electrodes. This trapped-ion sensor could be combined with other surface characterization tools to help elucidate the mechanisms that give rise to electric-field noise from ion-trap surfaces. Such noise presents a significant hurdle for performing large-scale trapped-ion quantum computations.