Briscoe was the son of Abraham William Briscoe and Ida Yoedicke, both of whom were Lithuanian-Jewish immigrants.The original family name in Lithuania is believed to have been Cherrick.
Bob and wife Lilly had seven children. Only two sons, Ben and Joe, remained in Dublin. Ben followed his father into politics, while Joe joined the army and rose to the rank of Commandant.
Briscoe was active in the Irish Republican Army (IRA) and Sinn Féin during the Irish War of Independence and accompanied Éamon de Valera to America. He spoke for the Sinn Féin cause at public meetings there and was adamant that being a "Hebrew" did not lessen his Irishness. Briscoe was sent by Michael Collins to Germany in 1919 to be the chief agent for procuring arms for the IRA. Eamon Martin, former Chief of Staff of Fianna Éireann, was best man at Briscoe's wedding. They had been close friends during the Irish War of Independence.
During the Second World War, Briscoe, at this time a member of Dáil Éireann, came under close scrutiny from the Irish security services. His support for Zionism and his lobbying on behalf of refugees was considered potentially damaging to the interests of the state by officials from the Department of Justice. Briscoe was an admirer and friend of Ze'ev Jabotinsky and his campaign to liberate the Jews. Between 1939 and 1940, Robert Briscoe along with John Henry Patterson, a former commander of the 4th battalion Royal Irish Fusiliers and the Zion Mule Corps, were involved in fund raising for the Irgun in the USA. Jabotinsky while head of Irgun visited Dublin to receive training in guerrilla warfare tactics against the British under the instruction of Briscoe. During the period Briscoe described himself as the "Chair of Subversive Activity against England". He wished for Ireland to give asylum to Jews fleeing Nazi Germany, but did so discreetly in order not to be accused of compromising the neutrality policy of the Fianna Fáil government.
He served in Dáil Éireann for 38 years and was elected 12 times in the Dublin South and from 1948, Dublin South–West constituencies - from the 6th Dáil to the 17th Dáil. He retired at the 1965 election, being succeeded by his son, Ben, who served for a further 37 years.
In 1956, Briscoe became the first Jewish Lord Mayor of Dublin, although he was not the first Jewish Mayor in Ireland. That title belongs to William Annyas, who was elected Mayor of Youghal, County Cork in 1555. Briscoe served a one year term and was re-elected in 1961.
After learning of a Jewish Lord Mayor from Dublin, Yogi Berra allegedly said, "Only in America!" His son Ben Briscoe was also a Fianna Fáil TD, and he too served as Lord Mayor of Dublin from 1988–1989.
His memoir, "For the Life of Me", was published in 1958.
The Emerald Isle immigration center in New York has devoted a special award in his name called the Robert Briscoe award. The group celebrates the close relationship between Jewish and Irish communities in New York and honors Jewish New Yorkers who have helped support immigration in the United States. The latest winner of the award was US Senator Chuck Schumer.