DNA nanotechnology has emerged as a powerful approach to engineering biophysical tools, therapeutics, and diagnostics because it enables the construction of designer nanoscale structures with high programmability. Based on DNA base pairing rules, nanostructure size, shape, surface functionality, and structural reconfiguration can be programmed with a degree of spatial, temporal, and energetic precision that is difficult to achieve with other methods. However, the properties and structure of DNA constructs are greatly altered due to spontaneous protein adsorption from biofluids. These adsorbed proteins, referred to as the protein corona, remain challenging to control or predict, and subsequently, their functionality and fate are difficult to engineer. To address these challenges, we prepared a library of diverse DNA nanostructures and investigated the relationship between their design features and the composition of their protein corona. We identified protein characteristics important for their adsorption to DNA nanostructures and developed a machine-learning model that predicts which proteins will be enriched on a DNA nanostructure based on the DNA structures' design features and protein properties. Our work will help to understand and program the function of DNA nanostructures for biophysical and biomedical applications.