DNA-stabilized silver clusters (Ag:DNAs) have attracted much attention due to their unique sequence-dependent fluorescence and many potential applications; however, the understandings of their atomic structures and functional properties are still limited, which hamper the further development of the novel nanoclusters. Using the advanced computational methods, we propose three atomistic models for the Ag:DNAs, which all contain a four-electron silver core with a two-row planar shape stabilized by the nitrogen atoms in the DNA. By comparing experimental and time-dependent density functional theory-simulated circular dichroism spectra, we have confirmed that these core structures should commonly exist in the Ag:DNAs. We then analyze the electronic and optical properties of the clusters and discover that the silver to DNA transitions have essential contributions to the chiroptical properties of the clusters.