The 21-year-old was left in a "stable but serious condition" after a fall while studying at the University of Washington.
Thornton, who represented Great Britain at the 2018 World Rowing Championships in Plovdiv, is set to return to her home town of Nottingham for further treatment and rehabilitation.
A statement released by the fundraiser, Pulling for Anna Thornton, revealed that any money raised by the website would be used to assist with her care programme.
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It said: "It is our hope that Anna’s incredible community of supporters will help raise the funds needed to provide the rehabilitation and skilled nursing care she needs."
Thornton defended her double scull title at the World Under 23 Championships in July in Poznan and represented Great Britain at the 2014 Youth Olympic Games in Nanjing.
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