  The positions and velocities of stellar streams have been used to constrain
the mass and shape of the Milky Way's dark matter halo. Several extragalactic
streams have already been detected, though it has remained unclear what can be
inferred about the gravitational potential from only 2D photometric data of a
stream. We present a fast method to infer halo shapes from the curvature of 2D
projected stream tracks. We show that the stream curvature vector must point
within 90 deg of the projected acceleration vector, in the absence of recent
time-dependent perturbations. While insensitive to the total magnitude of the
acceleration, and therefore the total mass, applying this constraint along a
stream can determine halo shape parameters and place limits on disk-to-halo
mass ratios. The most informative streams are those with sharp turns or flat
segments, since these streams sample a wide range of curvature vectors over a
small area (sharp turns) or have a vanishing projected acceleration component
(flat segments). We apply our method to low surface brightness imaging of NGC
5907, and find that its dark matter halo is oblate. Our analytic approach is
significantly faster than other stream modeling techniques, and indicates what
parts of a stream contribute to constraints on the potential. The method
enables a measurement of dark matter halo shapes for thousands of systems using
stellar stream detections expected from upcoming facilities like Rubin and
Roman.
