The sea ice surface is thought to be a major source of sea salt aerosol, suggesting that sodium records of polar ice cores may trace past sea ice extent. Here we test this possibility for the Arctic, using a chemical transport model to simulate aerosol emission, transport, and deposition in the satellite era. Our simulations suggest that sodium records from inland Greenland ice cores are strongly influenced by the impact of meteorology on aerosol transport and deposition. In contrast, sodium in coastal Arctic cores is predominantly sourced from the sea ice surface and the strength of these aerosol emissions controls the ice core sodium variability. Such ice cores may therefore record decadal to centennial scale Holocene sea ice changes. However, any relationship between ice core sodium and sea ice change may depend on how sea ice seasonality impacts sea salt emissions. Field‐based observations are urgently required to constrain this.