The transport of angular momentum due to neutral atoms in the tokamak edge is calculated and shown to be sensitive to the poloidal location of the neutrals. In the absence of external momentum sources, the edge plasma is predicted to rotate spontaneously in the opposite direction to the plasma current, at a speed proportional to the radial ion temperature gradient. If the plasma is collisional, this countercurrent rotation is largest if the neutrals are concentrated on the inboard side of the torus, while the opposite holds in a collisionless plasma. The presence of heavy impurity ions also promotes countercurrent rotation. The rotation caused by an external momentum source, such as neutral-beam injection, is found to be larger when the neutrals are on the inboard rather than the outboard side.