Is one of Russia’s oldest allies slipping from the Kremlin’s orbit?

The arrival of US soldiers for a peacekeeper training exercise in Armenia has rankled the Russian government, which has for decades acted as the sole security guarantor for the former Soviet republic. The 10-day “Eagle Partner” exercise, which began Monday, involves 85 US and 175 Armenian soldiers and aims to prepare the Armenians to take part in international peacekeeping missions.

The exercise, while small in scale, is the latest in a series of what Russia’s foreign ministry has deemed “unfriendly actions” taken by its traditional ally.

Armenia recently sent humanitarian aid to...