The U.S. Navy Merchant Marine Naval Reserve Pennant, which per 10 U.S.C. § 7225 can be flown by vessels which have been designated by the Secretary of the Navy as suitable as a naval auxiliary vessel in time of war, and the commanding officer and at least half the officers are members of the U.S. Navy.

The flag was first defined by U.S. Navy General Order No. 285, on April 14, 1917.  Today's version of the pennant is basically the same, except the eagle's head is turned the other way.  I have seen an EBay auction of a World War II-era version, which still had the head facing to its left, so the change happened after that time (similarly, the eagle's head direction was switched on the Flag of the President of the United States shortly after the war).  For more information, see SeaFlags, and Navy Document NTP-13(B), section 1717.
Modified from File:USN-MerchantMarineNavalReserveFlag-1917.svg.  The low-resolution drawings in the Navy NTP-13 (B) document look identical to the original other than the head direction, so that is the only change in this version.
Carl Lindberg