The need to monitor changes in the level of agricultural competitiveness of EU member states necessitates the development of an appropriate set of indicators to answer the question of whether a country is improving its competitive position. This paper proposes a synthetic measure for assessing the agricultural competitiveness in the member states of the European Union (EU) from 2012 to 2021. Statistics on the respective indicators were derived from the Eurostat database and Agri-Food Data Portal. The survey was based on linear ordering using a standardised sums approach. This implies that member states vary in competitiveness in the agricultural sector. From 2012 to 2021, the most competitive countries were Denmark, the Netherlands, and Belgium. Simultaneously, the rankings of agricultural competitiveness changed over the 10 years under review. The highest improvement rates were recorded in Finland, Slovakia, and Ireland. However, the differences between the old and new member states are still explicit. None of the new member states of the EU were in the top ten with regard to their agricultural competitiveness. Many areas associated with agriculture in these countries require considerable improvement. We also carried out a principal component analysis (PCA), which allowed us to identify the parameters conveying relevant information on the analysed phenomenon and unveil the hidden structures in the primary data set. We discovered that the share of the EU’s agricultural output in the EU exports of agricultural products explained variations in the agricultural competitiveness within member states.