Rao has been awarded as Fellow of National Academy of Sciences, India in 2001 and Fellow of the Indian Academy of Sciences in 2017 for her contributions in the theoretical condensed matter physics. She was named a Fellow of the American Physical Society in 2022 "for contributions to transport in low-dimensional interacting systems, especially junctions of more than two wires, edge/surface physics of topological systems, and for contributions to overcoming the under-representation of women in physics".