This paper focuses on the polarized profiles of resonance scattering lines that form in magnetized disks. Optically thin lines from Keplerian planar disks are considered. Model line profiles are calculated for simple field topologies of axial fields (i.e., vertical to the disk plane) and toroidal fields (i.e., purely azimuthal). A scheme for discerning field strengths and geometries in disks is developed based on Stokes Q − U diagrams for the run of polarization across line profiles that are Doppler-broadened by the disk rotation. A discussion of the Hanle effect for magnetized disks in which the magnetorotational instability (MRI) is operating is also presented. Given that the MRI has a tendency to mix the vector field orientation, it may be difficult to detect the disk fields with the longitudinal Zeeman effect, since the amplitude of the circularly polarized signal scales with the net magnetic flux in the direction of the observer. The Hanle effect does not suffer from this impediment, and so a multi-line analysis could be used to constrain field strengths in disks dominated by the MRI.