The damped Ly-alpha and 21 cm absorption-line quasar PKS 1229-021 (z = 1.038) has been mapped in detail with the VLA at seven frequencies, with polarimetry. It has a radio jet, whose rotation measure distribution at 0".46 shows a clear and strong "oscillation" over its length, which is approximately 35h65 kpc at the absorption-line red-shift of 0.395. This new, extended, intervenor probe combined with the optical absorption spectrum, well studied by Briggs and coworkers, suggests that the intervenor at z = 0.395 is a "bisymmetric magnetic field" spiral galaxy, possibly similar to M81. This galaxy is 200 times farther than the previous most distant galaxy whose large-scale magnetic field has been mapped. A detailed analysis of the combined radio Faraday rotation and the absorption spectrum of PKS 1229-021 enables us, assuming an intervening spiral galaxy disk, to specify the orientation, inclination, magnetic field reversal scale, and magnetic field strength in the intervenor of PKS 1229-021. Our model also predicts the position of its nucleus (which has not yet been seen optically) relative to the QSO. Both the strength and the reversal scale of the magnetic field appear similar to those recently determined for nearby galaxies. We estimate a magnetic field strength of order 1-4-mu-G. We briefly discuss the implications of the existence of a bisymmetric spiral (m = 1) field at z = 0.395 for possible values of seed fields on the assumption that the galaxy field was amplified by a dynamo.