In 1976 Barton sought election as the Congressman from the First District, beating six other candidates in the Democratic primary but losing to the incumbent, Republican David F. Emery.

Barton's diplomatic career began in 1990, when he was selected as an election trainer and observer in Haiti for the National Democratic Institute (NDI) and also volunteered in Poland and Ethiopia.

In 1994, he became the founding director of the Office of Transition Initiatives (OTI) within the U.S. Agency for International Development (USAID), to advance peaceful democratic change in conflict-prone places such as Bosnia, Rwanda, Haiti, Liberia, and Mindanao in the Philippines.

Barton was appointed Deputy High Commissioner of the United Nations Refugee Agency (UNHCR) in Geneva, Switzerland in 1999, serving under Sadako Ogata and then Ruud Lubbers.

From 2002 to 2009 Barton was Co-Director of the Post-Conflict Reconstruction Project at the Center for Strategic and International Studies (CSIS), where he served as an expert adviser to the Iraq Study Group, led conflict-related working groups for the United States Institute of Peace and the Princeton Project on National Security, and produced reports on Iraq, Afghanistan, Sudan, Pakistan, religion in conflict, measurement of progress, and U.S. legislative policy.

Barton's work at the UN and CSO led to a 2013 Distinguished Honor Award from the Department of State in recognition of his "groundbreaking work to create the Bureau of Conflict and Stabilization Operations, promote peacebuilding and empower women, youth and other change agents seeking peaceful change in their communities and societies" including Nigeria, Syria, Honduras, Burma and Kenya.