We present a ballistic rectification effect in an orthogonal four-terminal cross junction where the symmetry is broken by local magnetic fields. The input current is injected between opposing branches and the current-free branches serve as potential probes. The local magnetic field is induced by two permalloy (Py) stripes with a magnetic single-domain structure, where one end of each stripe is positioned close to the junction center. The Py stripes are oriented such that an external in-plane magnetic field can magnetize them into two different main configurations having either equally or oppositely magnetized ends. Equal magnetic ends are expected to result in a Hall-effect device, while for opposite magnetic ends, the stray field should deflect the electrons into the same output lead for both current polarities, leading to a rectifying behavior. Here, we present the proof of concept for stray-field controlled transfer characteristics. First, we show by magnetic force microscopy that both configurations are stable and the Py stripes exhibit a remanent magnetic single-domain structure. Second, we demonstrate the influence of the remanent magnetization on the low-temperature dc characteristics which are superimposed by a parasitic background. Third, we present the extracted Hall and the rectified voltage which are, respectively, linearly and parabolically dependent on the input current up to ±55 μA.