Only reference I could find. A Senator no, member of a Senators staff is allowed:
On May 25, 1994, this office issued an opinion advising that the appointment of a United States Senator as a DUSM would be inconsistent with separation of powers principles.(1) We primarily based that conclusion upon "the principle recognized in Bowsher v. Synar, 478 U.S. 714 (1986), that Congress may not exceed its constitutionally prescribed authority by playing a direct role in executing the laws." 18 Op. O.L.C. at . Although such an appointment might raise additional problems under the Incompatability Clause of Article I, section 6, we did not reach that issue in the earlier opinion. See U.S. Const. art. I, ยง 6, cl. 2.
We were subsequently asked whether the deputation of an employee on the personal staff of a U.S. Senator, for purposes of providing protection and personal security against threatened violence(2), would be constitutionally permissible. We concluded that it would. Our views on that issue were reflected in a Memorandum from the Director of the United States Marshals Service ("USMS") to you, reviewed and endorsed by this office, dated January 26, 1995. Memorandum for the Deputy Attorney General, from Eduardo Gonzalez, Director, United States Marshal Service, Re: Continued Deputation (Jan. 26, 1995) ("Joint Memorandum"). In concluding that deputation of the congressional staff member would not violate the separation of powers, the Joint Memorandum stated:
The deputized staff person is not a Member of Congress and exercises no legislative power under Article I of the Constitution; nor would Congress (or any member thereof) have the authority to grant or revoke his appointment as a special DUSM, or to control or supervise his official duties as such.
http://www.justice.gov/olc/usmsdep_sa1.htm