Local curvatures on the cell membrane serve as signaling hubs that promote curvature-dependent protein interactions and modulate a variety of cellular processes including endocytosis, exocytosis, and the actin cytoskeleton. However, precisely controlling the location and the degree of membrane curvature in live cells has not been possible until recently, where studies show that nanofabricated vertical structures on a substrate can imprint their shapes on the cell membrane to induce well-defined curvatures in adherent cells. Nevertheless, the intrinsic static nature of these engineered nanostructures prevents dynamic modulation of membrane curvatures. In this work, we engineer light-responsive polymer structures whose shape can be dynamically modulated by light and thus change the induced-membrane curvatures on-demand. Specifically, we fabricate threedimensional azobenzene-based polymer structures that change from a vertical pillar to an elongated vertical bar shape upon green light illumination. We observe that U2OS cells cultured on azopolymer nanostructures rapidly respond to the topographical change of the substrate underneath. The dynamically induced high membrane curvatures at bar ends promote local accumulation of actin fibers and actin nucleator Arp2/3 complex. The ability to dynamically manipulate the membrane curvature and analyze protein response in real-time provides a new way to study curvature-dependent processes in live cells.