We report radio polarization observations of G319.9-0.7 (MSC 319.9-0.7) at 3 and 6 cm obtained with the Australia Telescope Compact Array. The source shows a highly elongated morphology with the energetic pulsar J1509-5850 located at the tip. We found a flat radio spectrum of index \alpha=-0.26 +/- 0.04 and a high degree of linear polarization. These results confirm G319.9-0.7 as a bow-shock pulsar wind nebula. The polarization maps suggest a helical magnetic field trailing the pulsar, with the symmetry axis parallel to the system's inferred direction of motion. This is the first time such a field geometry has been seen in a bow-shock nebula, and it may be the result of an alignment between the pulsar spin axis and its space velocity. Compared to other bow-shock examples, G319.9-0.7 exhibits very different properties in the field structure and surface brightness distribution, illustrating the large diversity of the population.