Cell entry of anionic nano-objects has been observed in various types of viruses and self-assembled DNA nanostructures. Nevertheless, the physical mechanism underlying the internalization of these anionic particles across the negatively charged cell membrane remains poorly understood. Here, we report the use of virus-mimicking designer DNA nanostructures with near-atomic resolution to program "like-charge attraction" at the interface of cytoplasmic membranes. Single-particle tracking shows that cellular internalization of tetrahedral DNA nanostructures (TDNs) depends primarily on the lipid-raft-mediated pathway, where caveolin plays a key role in providing the short-range attraction at the membrane interface. Both simulation and experimental data establish that TDNs approach the membrane primarily with their corners to minimize electrostatic repulsion, and that they induce uneven charge redistribution in the membrane under the short-distance confinement by caveolin. We expect that the nanoscale like-charge attraction mechanism provides new clues for viral entry and general rules for rational design of anionic carriers for therapeutics.