Reducing greenhouse gas emissions from agriculture is crucial to reach global and regional climate targets. However, the efficiency of unilateral climate policies aimed at taxing emissions might be hampered by carbon leakage. One way to eliminate leakage is to implement a global carbon tax. In this article, we study the effects of a carbon tax in agriculture on GHG emissions by simulating five policy scenarios using the CAPRI model; (i) an EU tax, (ii) an EU tax complemented with a border carbon adjustment mechanism (BCA), (iii) a global tax, (iv) a global tax scaled by GDP per capita, and (v) a low global tax at 1/10 of the tax level in the other scenarios. For the global scenarios, we also analyse the impact on food consumption and nutrient intake. We find that a global tax of EUR 120 per ton CO2-eq could reduce global agricultural emissions by 19%, but also jeopardizes food security in some parts of the world. A global tax at 1/10 of that rate (EUR 12) achieves a 3.2% reduction. In contrast, a unilateral EU tax of EUR 120 per ton CO2-eq, accompanied with a BCA, reduces global agricultural emissions by only 0.15%.