The surname Rink was first found in Norfolk where conjecturally, the surname is descended from the tenant of the lands of Ringstead, held by Norman noble Roger de Evreux as an under tenant also at Great Bircham and Old Buckenham in that same county who was recorded in the Domesday Book census of 1086. Roger held from William de Scohies who was tenant in chief. Roger was the son of Comte de Evreux, who was the son of Richard 1, Duke of Normandy.
Roger Ringstead (died 1366), was Bishop of Bangor, perhaps a native of Ringstead in Norfolk, educated at Cambridge, where he became doctor and professor of theology. 
Early History of the Rink family
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^ Smith, George (ed), Dictionary of National Biography. London: Smith, Elder & Co., 1885-1900. Print
^ Filby, P. William, Meyer, Mary K., Passenger and immigration lists index : a guide to published arrival records of about 500,000 passengers who came to the United States and Canada in the seventeenth, eighteenth, and nineteenth centuries. 1982-1985 Cumulated Supplements in Four Volumes Detroit, Mich. : Gale Research Co., 1985, Print (ISBN 0-8103-1795-8)