Abstract. Galactic cosmic rays (GCRs) interact with matter in the atmosphere and at the surface of the Earth to produce a range of cosmogenic nuclides. Measurements of cosmogenic nuclides produced in surface rocks have been used to study past land ice extent as well as to estimate erosion rates. Because the GCR flux reaching the Earth is modulated by magnetic fields (solar and Earth's), records of cosmogenic nuclides produced in the atmosphere have also been used for studies of past solar activity. Studies utilizing cosmogenic nuclides assume that the GCR flux is constant in time, but this assumption may be uncertain by 30 % or more. Here we propose that measurements of 14C of carbon monoxide (14CO) in ice cores at low-accumulation sites can be used as a proxy for variations in GCR flux on timescales of several thousand years. At low-accumulation ice core sites, 14CO in ice below the firn zone originates almost entirely from in situ cosmogenic production by deep-penetrating secondary cosmic ray muons. The flux of such muons is almost insensitive to solar and geomagnetic variations and depends only on the primary GCR flux intensity. We use an empirically constrained model of in situ cosmogenic 14CO production in ice in combination with a statistical analysis to explore the sensitivity of ice core 14CO measurements at Dome C, Antarctica, to variations in the GCR flux over the past ≈ 7000 years. We find that Dome C 14CO measurements would be able to detect a linear change of 6 % over 7 ka, a step increase of 6 % at 3.5 ka or a transient 100-year spike of 190 % at 3.5 ka at the 3σ significance level. The ice core 14CO proxy therefore appears promising for the purpose of providing a high-precision test of the assumption of GCR flux constancy over the Holocene.