Wiener graduated cum laude from Brown University in 1927, and magna cum laude from Harvard Law School, where he was note editor for the Harvard Law Review, in 1930. He was admitted to the bar of Rhode Island the next year, and the Supreme Court bar in 1934.

During World War II, he served in the Judge Advocate General's Corps, retiring from the United States Army in 1966 with the rank of Colonel. Working for the Solicitor General's Office and later in private practice, he often argued before the U.S. Supreme Court.

From 1951-1956, he lectured in law at George Washington University, while also lecturing before foreign and domestic groups. In 1962 he was awarded a Guggenheim Fellowship. He retired from active practice in 1973 while continuing occasional consultations. In 1974, he was awarded the U.S. Army's Outstanding Civilian Service Medal.

Wiener was called no less than seven times to testify before Congress on matters pertaining to military law. On 6 August 1984, he testified before the United States Senate Governmental Affairs Subcommittee on Civil Service, Post Office and General Services, chaired by Senator Ted Stevens, against the passage of S.2116, a bill which, based on the findings of the Relocation Commission, sought to provide an apology and financial reparations to Japanese-Americans who had been interned during World War II. Wiener testified that the Commissions report contained numerous misstatements and omissions that led to erroneous conclusions, in part because several of the Commissioners had made up their minds before the investigation began. The bill died in committee without coming up for a vote.