Arnn has been a trustee of the conservative Heritage Foundation since 2002. In 2012 it offered its presidency to Arnn, who decided to stay in academe instead.
Arnn also sits on the boards of directors of the Henry Salvatori Center for the Study of Individual Freedom in the Modern World at Claremont McKenna College, the Center for Individual Rights, and the Claremont Institute. He is a member of the Mont Pelerin Society, the Churchill Centre, and the Philanthropy Roundtable. As of 2014, he was listed as a member of the Council for National Policy in their directory.
Discussing politics at Hillsdale, Arnn remarked, "If you take the reading of an old book on the view that it's valuable, you have already discarded the modern Left." Arnn supported Donald Trump for President in the 2016 US election.