Abstract Objects orbiting in the presence of a rotating massive body experience a gravitomagnetic frame-dragging effect, known as the Lense-Thirring effect, that has been experimentally confirmed in the weak-field limit. In the strong-field limit, near the horizon of a rotating black hole, frame dragging becomes so extreme that all objects must co-rotate with the black hole’s angular momentum. In this work, we perform general relativistic numerical simulations to identify observable signatures of frame dragging in the strong-field limit that appear when infalling gas is forced to flip its direction of rotation as it is being accreted. In total intensity images, infalling streams exhibit “S”-shaped features due to the switch in the tangential velocity. In linear polarization, a flip in the handedness of spatially resolved polarization ticks as a function of radius encodes a transition in the magnetic field geometry that occurs due to magnetic flux freezing in the dragged plasma. Using a network of telescopes around the world, the Event Horizon Telescope collaboration has demonstrated that it is now possible to directly image black holes on event horizon scales. We show that the phenomena described in this work would be accessible to the next-generation Event Horizon Telescope and extensions of the array into space, which would produce spatially resolved images on event horizon scales with higher spatial resolution and dynamic range.