The solar corona's magnetic field governs much of our space environment's structure and dynamics, yet measuring it remains notoriously difficult. We established a novel approach that combines polarized coronal emission with the magnetic constraints encoded in propagating Alfvénic waves. We theoretically demonstrate the feasibility of recovering the full 3D magnetic field across the off-limb corona without relying on difficult-to-measure Stokes V signals. We then demonstrate its practical application using MLSO CoMP and UCoMP observations of the Fe XIII infrared emission lines. The results demonstrate a new route toward routine, wide-field mapping of the Sun’s otherwise hidden coronal magnetic field.