In the assembly of DNA nanostructures, the specificity of Watson-Crick base pairing is used to control matter at the nanoscale. Using this technology for drug delivery is a promising route toward the magic bullet concept, as it would allow the realization of complex assemblies that co-localize drugs, targeting ligands and other functionalities in one nanostructure. Anthracyclines' mechanism of action in cancer therapy is to intercalate DNA, and since DNA nanotechnology allows for such a high degree of customization, we hypothesized that this would allow us to tune the DNA nanostructures for optimal delivery of the anthracycline doxorubicin (Dox) to human breast cancer cells. We have tested two DNA origami nanostructures on three different breast cancer cell lines (MDA-MB-231, MDA-MB-468, and MCF-7). The different nanostructures were designed to exhibit varying degrees of global twist, leading to different amounts of relaxation in the DNA double-helix structure. By tuning the nanostructure design we are able to (i) tune the encapsulation efficiency and the release rate of the drug and (ii) increase the cytotoxicity and lower the intracellular elimination rate when compared to free Dox. Enhanced apoptosis induced by the delivery system in breast cancer cells was investigated using flow cytometry. The findings indicate that DNA origami nanostructures represent an efficient delivery system for Dox, resulting in high degrees of internalization and increased induction of programmed cell death in breast cancer cells. In addition, by designing the structures to exhibit different degrees of twist, we are able to rationally control and tailor the drug release kinetics.