Ice shelves are floating extensions of grounded ice and play a crucial role in slowing ice discharge into the ocean. Ice flows in response to stresses according to the flow law, which is essential for predicting the mass loss of ice sheet. Laboratory experiments have shown that polycrystalline ice obeys Glen’s flow law, a power-law relation between the stress and strain rate that has been applied to ice-sheet models for decades. However, it remains unclear how processes at ice-shelf scales impact the flow law, i.e. rheology, of glacial ice. Here, we reveal the rheology of glacial ice in Antarctic Ice Shelves leveraging the availability of remote-sensing data and physics-informed deep learning. We find that the rheology of ice shelves differs substantially between the compression and extension zones. In the compression zone near the grounding line the rheology of ice closely obeys power laws with exponents in the range 1 < n < 3, consistent with prior laboratory experiments. In the extension zone, which comprises most of the total ice-shelf area, the rheology deviates from laboratory findings and does not follow a clear trend. Our result highlights a need to examine the impact of ice-shelf scale processes on glacial rheology.