Bids for the 1963 model began on Monday afternoon (11Aug14) and will end on what would have been the punk icon's 62nd birthday on 21 August (14).
The rocker passed away on 22 December, 2002. He purchased the classic car in 1987 for $4,200 (Gbp2,470).
The vehicle remains in pristine condition as it has been housed in a climate controlled garage.
Beverly Hills Car Club owner Alex Manos tells Wenn, "This is such a special car to me. I knew Joe Strummer as a boy growing up in London. He was one of a kind, just like this car.
"Joe had an enormous love for American cars and I feel it’s serendipitous that this beautiful 1963 Ford Thunderbird is coming to us for sale."