Radcliffe, 16, who plays the schoolboy wizard on screen, bought a handwritten history of the family of Sirius Black, his character's godfather.
Rowling donated the document to the sale by Book Aid International, which provides books for schools in Africa.
JK Rowling was among 45 writers to donate work for auction
The actor also successfully bid for handwritten works by writers Iain Banks and Tom Stoppard, totalling 4,680.
Radcliffe's mother Marcia Gresham bid on his behalf at the central London auction.
She said: "This should put paid to anyone who says that Daniel doesn't like reading.
"Daniel hasn't stopped since he read the first Harry Potter book and he loves Iain Banks and Tom Stoppard."
Donated documents
The star bought a short Stoppard play entitled Murder for 3,700 and a humorous piece on writing by Banks for 980.
Book Aid International also donates books to African hospitals, universities and refugee camps.
The charity's director Sara Harrity said: "We raised more than 63,000 - more than we had hoped in our wildest dreams."
Other literary figures to donate works included crime author PD James, children's writer Jacqueline Wilson and actress Joanna Lumley, who published her autobiography in 2004.
Gary Oldman played Sirius Black in the two most recent films in the series, Harry Potter and the Prisoner of Azkaban and Harry Potter and the Goblet of Fire.