In most junctions built by wiring a single molecule between two electrodes, the electrons flow along only one axis: between the two anchoring groups. However, molecules can be anisotropic, and an orientation-dependent conductance is expected. Here, we fabricated single-molecule junctions by using the electrode potential to control the molecular orientation and access individual elements of the conductivity tensor. We measured the conductance in two directions, along the molecular plane as the benzene ring bridges two electrodes using anchoring groups (upright) and orthogonal to the molecular plane with the molecule lying flat on the substrate (planar). The perpendicular (planar) conductance is about 400 times higher than that along the molecular plane (upright). This offers a new method for designing a reversible room-temperature single-molecule electromechanical switch that controllably employs the electrode potential to orient the molecule in the junction in either "ON" or "OFF" conductance states.