Yes they can, and yes they have in the past...the 4th Congress declared war on the Barbary Pirates - an autonomous group.
As far as I can tell, Congress declared war on the city-state of Tripoli:
Tripolitan War (1801-1805), conflict between the United States and the North African state of Tripoli (now in Libya). For centuries the Muslim corsairs of North Africa either had preyed on the shipping of Christian nations or demanded tribute. The U.S. had been paying tribute since 1784, but refused to agree to an increase demanded by the pasha of Tripoli in 1801. As a result, the Tripolitans began seizing American ships, and in 1803 a U.S. naval squadron was sent to blockade the port of Tripoli. When the U.S. frigate Philadelphia was captured and taken into the harbor in February 1804, a small group of men under Lieutenant Stephen Decatur managed to reach it in a daring night raid and burn it to prevent the corsairs from using it. The war ended in 1805, when Captain William Eaton led 500 men across the desert from Alexandria and captured the Tripolitan town of Darnah. The pasha agreed to make peace, abandoning his demands for tribute but exacting a ransom of $60,000 for freeing American captives. A sequel to the Tripolitan War was the U.S. expedition against the corsairs of Algiers in 1815.I spent a fair amount of time at the web site of the National Archives, trying to find the text of the declaration, but that web site is worthless.