The design of more efficient photosensitizers is a matter of great importance in the field of cancer treatment by means of photodynamic therapy. One of the main processes involved in the activation of apoptosis in cancer cells is the oxidative stress on DNA once a photosensitizer is excited by light. As a consequence, it is a matter of great relevance to investigate in detail the binding modes of the chromophore with DNA, and the nature of the electronically excited states that participate in the induction of DNA damage, for example, charge-transfer states. In this work, we investigate the electronic structure of the anthraquinone photosensitizer intercalated into a double-stranded poly(dG-dC) decamer model of DNA. First, the different geometric configurations are analyzed by means of classical molecular dynamics simulations. Then, the excited states for the most relevant poses of anthraquinone inside the binding pocket are computed by an electrostatic-embedding quantum mechanics/molecular mechanics approach, where anthraquinone and one of the nearby guanine residues are described quantum mechanically to take into account intermolecular charge-transfer states. The excited states are characterized as monomer, exciton, excimer and charge-transfer states based on the analysis of the transition density matrix, and each of these contributions to the total density of states and absorption spectrum is discussed in terms of the stacking interactions. These results are relevant as they represent the footing for future studies on the reactivity of anthraquinone derivatives with DNA and give insights on possible geometrical configurations that potentially favor the oxidative stress of DNA.