The orientation of the local interstellar magnetic field introduces asymmetries in the heliosphere that affect the location of heliospheric radio emissions and the streaming direction of ions from the termination shock of the solar wind. We combined observations of radio emissions and energetic particle streaming with extensive three-dimensional magnetohydrodynamic computer simulations of magnetic field draping over the heliopause to show that the plane of the local interstellar field is ∼60° to 90° from the galactic plane. This finding suggests that the field orientation in the Local Interstellar Cloud differs from that of a larger-scale interstellar magnetic field thought to parallel the galactic plane.