Radcliffe was born on a farm at Lloyds, near Cambridge, Maryland. He attended both public and private schools in his youth and later graduated from Cambridge Seminary in 1893, from Johns Hopkins University in 1897, from the graduate school of Johns Hopkins University in 1900, and from the law department of the University of Maryland, Baltimore in 1903.

Following college, Radcliffe took the position of principal of the Cambridge Seminary he had attended as a youth. After a stint as a teacher in the Baltimore City College in 1901 and 1902, Radcliffe was admitted to the bar in 1903 and commenced practice in Baltimore, Maryland with an interest in banking and farming.

During the First World War, Rafcliffe joined the Liquor License Commission in Baltimore, serving from 1916-1919, and also served as a member of the Maryland State Council of Defense. In 1919, Radcliffe was selected as secretary of state of Maryland and served until 1920. In 1933 and again in 1934, Radcliffe was chosen regional adviser of the Public Works Administration for Maryland, Delaware, Virginia, West Virginia, North Carolina, Tennessee, Kentucky, and the District of Columbia.

In the election of 1934, Radcliffe was elected as a Democrat to the United States Senate, and was subsequently reelected in the 1940 election. Radcliffe failed to achieve re-nomination for his party in the election of 1946, losing to fellow Democrat Herbert R. O'Conor.

Radcliffe resumed banking and farming interests following his tenure as senator and was actively involved in civic life. He resided in Baltimore until he died, and is buried at the Cambridge Cemetery in his hometown.

This article incorporates facts obtained from the public domain Biographical Directory of the United States Congress.