If magic were to spontaneously manifest, I don't believe that the reaction of the US would be to create an entirely new Executive Department for dealing with it. Rather, the mandates of the existing Departments would likely expand - and organizations would be created within them to handle issues relating to it. There would also be a bit of internal politicking concerning who exactly has what operating authority in what areas to what extent.
The concerns of the Agency would also likely vary based on what the magical system is actually capable of, where it comes from, and who has access to it. This would also highly shift which organizations have the most operational authority in areas dealing with magic.
In the US, Defense is the 4th highest category of Federal Spending - with an extensive research and development arm and a very broad mandate the first response will likely come from the Department of Defense. Assessment and Categorizing of the potential threat and utility of the magic system would likely be the primary concern. The Military Departments and the Intelligence Community would most likely be the first to task.
Following the Military (in no particular order) the Department of Justice and the Department of Homeland Security. In these organizations exist the US Secret Service, as well as the FBI and ATF. These three organizations have historically expanded their mandates - and would be likely to take in handling issues of illicit magic use. My money would be on the Secret Service first - their position previously in the Department of Treasury and now in Homeland Security allows them to act really quickly, eventually I think the tasks would be phased into other departments where relevant.
This would be the quickest way that a response to magic could happen within the US system. Sometime after the initial manifestation the Department of Magical Affairs would likely be formed, to take over the new excess tasks of new organizations - as well as various others.