We present the first results from the Atacama Large Millimeter/submillimeter Array Perseus Polarization Survey, focusing on the magnetic field in the SVS 13A circumbinary disk. The data set includes full Stokes dust continuum observations at ∼0.″3 and 870 μm, as well as molecular line emission from C17O(J = 3 → 2) at ∼0.″3 , C18O(J = 2 → 1) at ∼0.″2 , and DCN(J = 3 → 2) at ∼0.″1 angular resolution. Our observations resolve both a previously identified dust spiral and an infalling streamer, capturing their spatial and kinematic structures. The streamer is traced from scales >300 au down to the circumbinary disk. Using alignment measure (AM) maps and histograms that compare the orientations of the plane-of-sky magnetic field with local intensity and velocity gradients, we find that the AM distribution peaks at a value of 1. This AM peak strongly suggests alignment between the field and the dust total intensity emission, as well as between the field and the gas velocity, which in turn suggests grain alignment by magnetic fields. From our data, we derive a magnetic field strength, Bpos ∼ 1.1 ± 0.6 mG, and a kinetic-to-magnetic energy ratio of 0.5 ± 0.4, suggesting magnetic dominance. We also produced a map of the Alfvénic Mach number, finding MA<1 along the streamer, consistent with sub-Alfvénic infalling motions. Therefore, the field is likely facilitating the inflow of material from the envelope onto the disk by constraining movement across the field lines. This represents the first detection of a magnetically sub-Alfvénic infalling streamer in a protostellar system.