Under Article I, section 6, clause 2, I mean.
That Clause provides in pertinent part that “no Person holding any Office under the United States, shall be a Member of either House during his Continuance in Office.” Under this provision, known as the Incompatibility Clause, holding an office “under the United States” is deemed incompatible with service in the U.S. Congress.
Senator Graham serves in the U.S. Air Force Reserves. From time to time he has been called to active duty, including three “mini-tours” in Iraq. During one of his stints on active duty, the Judge Advocate General of the Air Force assigned Graham to sit as a judge on the Air Force Court of Criminal Appeals, an intermediate appellate court in the military justice system. In that capacity, Graham served in 2004 on a panel that upheld the conviction of an airman charged with drug use.
Senator Brown is a member of the Massachusetts Army National Guard. He also is called to active duty from time to time, including a recent week-long training stint in Afghanistan.
As military officers, albeit part-time and normally inactive, Graham and Brown might be thought to hold “office[s] under the United States” which would make them ineligible to serve in Congress under the Incompatibility Clause. There seems to be little question that the Incompatibility Clause applies to military offices and thus that regular active-duty officers in the United States military are prohibited from serving in Congress. See Note, “An Officer and a Congressman: The Unconstitutionality of Congressmen in the Armed Forces Reserve,” 97 Geo. L.J 1739, 1744-45 (2009) (collecting evidence that the Framers understood the Incompatibility Clause applies to military offices).