As Tom Brown has been ruled out until October with a knee injury, head coach Alan Solomons has brought 23-year-old Thompson in to provide cover for Tim Visser and Dougie Fife.
Thompson, whose Northern Ireland father Salty also played for the USA, was a regular in the American team in the HSBC Sevens World Series before making a try-scoring full international debut in a 38-35 win over Canada last month.
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The 6ft 4in player, whose move is subject to a medical, said: "It's always been a dream of mine to play at the top level. I'm ready to work hard and compete to help the team be successful in any way I can."
Solomons said: "Injuries and Scotland duty means we are stretched for specialist wingers and this addition relieves the pressure on the squad in that area. Brett has already showcased his talent on the international stage and we believe there is much more to come from him."