As of January 2015, the United States is not at war with the country of Syria. The United States has been leading a multinational coalition in conducting air strikes on extremist groups in the country, but is not formally at war with the country itself.
In September of 2014, the United States began conducting air strikes in Syria directed against ISIL forces and groups associated with al-Qaida. The United States is partnered with the United Arab Emirates, Jordan, Bahrain, Qatar and Saudi Arabia in this effort. This action followed from the kidnapping of a number of foreigners by ISIL forces in Syria in July of 2014 and a subsequent rescue operation that failed to recover the hostages and led to a number of them being beheaded publicly by ISIL. These air strikes have been carried out without permission of the Syrian government, but the Syrian United Nations representative was notified in advance, and the Syrian government has not acted to stop the strikes in any way.
The United States is not formally participating in the Syrian civil war between rebel forces and President Bashar Assad, though it has provided nonlethal aid to some rebel forces, and the CIA has reportedly been covertly training forces in the area.