This quick study shows two tall signs for fast food establishments. These are the kind of signs that you would usually see on an Interstate Highway, advertising an establishment to long-distance travelers approaching the exit.
First is the sign for a McDonalds at the corner of 9th and T Streets NE. It's in the middle of an area that's zoned industrial and commercial, with no residences for many blocks in every direction (map).
The second sign is for the Checkers just off of H Street in the northeast corner of Capitol Hill (map). This location is surrounded by residences, on the edge of the H Street commercial district.
I looked through the zoning regulations, expecting to find something that might hint that the Checkers sign would not be legal. It just seems so out of place in a residential neighborhood, especially one with the design rules of Capitol Hill. But the location is a few blocks north and east of the edge of the Capitol Hill Historic District, so the stricter rules that would probably preclude such signage don't apply here.