An accurate chronology of ice cores is still needed for interpreting the paleoclimatic record and to understand the relation between insolation and climate. A new domain of research in this area has been stimulated by the work of M. Bender linking the record of N₂/O₂ ratio in the air trapped in the ice with the local insolation. Here we investigate the potential of the air content of polar ice, V, as another and complementary ice proxy of local insolation. We propose that the long-term changes in air content recorded in ice from the high Antarctic plateau is dominantly imprinted by the local summer insolation. The V measurements covering the last 440,000 yr and obtained along the EPICA DC (EDC) ice core are presented. 86% of the variance observed in the V record can be explained neither by air pressure nor by temperature changes, and then should reflect properties influencing the porosity at close-off other than temperature. A wavelet analysis indicates a dominant obliquity period (around 41 ka) over the last 440 ka. We propose a mechanism, which can account for the observed anti-correlation between local insolation and V and explain how the local insolation, via the integrated summer insolation, can affect the near-surface snow structure and consequently the porosity at close-off. The V and the integrated summer insolation changes show high coherency over all the record and a variable phase relationship with a maximum phase difference of about 4000 yr around 200 ka ago. The phase difference may reflect the difference between the EDC2 chronology based on an inverse dating method and an accurately dated insolation curve. Our work, by proposing a new and complementary ice proxy for local insolation should eventually contribute to the establishment of an absolute dating of the ice paleo-record.