Fofonoff solutions to the inviscid barotropic potential vorticity equation are found for the steady, free flow in a basin rotated at an arbitrary angle to a latitude circle. These solutions am used to study the inertial recirculation of the subtropical gyre, which is forced by anomalously low values of potential vorticity within the separated Gulf Stream. It is found, depending on the sense of rotation of the northern boundary relative to latitude circles, that closed potential vorticity contours can exist that allow a large-amplitude inertial response, a resonance of the Fofonoff gyre. A barotropic ocean model is used to confirm thew ideas, in which flow is forced both by potential vorticity anomalies prescribed at the boundaries, and also a field of Ekman pumping, which spins up an anticyclonic gyre. It is shown that the recirculation is sensitive to both the orientation and extension of the inertial jet along the northern boundary.