It depends on how you take tides into account. The D River (variously measured between 120ft and 440ft) in Lincoln City, Oregon and the Roe River (measuring 201ft) in Great Falls, Montana are the two finalists, though.
The Roe River is the shortest river in the USA. It also doubles up as the shortest river in the world according to the Guinness book of records. It is in flows from the Giant Springs to the Missouri river in Montana.