There is concern that unilateral climate action in the EU agricultural sector may cause higher emissions abroad (i.e. emission leakage) and harm the competitiveness of the EU´s agricultural sector. Applying the CAPRI model, this paper assesses the potential for border carbon adjustments (BCA) in the form of import tariffs to limit the leakage of emissions and preserve the competitiveness of the EU agricultural sector. Our results show that even though BCA reduces emission leakage, 92 % of the emission reduction in the EU is still offset by emission increases outside the EU. What limits the effectiveness of the investigated BCA measures is that these measures are unilateral, and thus they only adjust for the reduced competitiveness at the EU internal market, whereas EU exports are still largely replaced by commodities produced in less GHG-efficient countries. Therefore, BCA alone cannot solve the high risk of emission leakage in the agri-food sector as a consequence of unilateral EU climate action.