Born in Glasgow, Roberton entered the family business of funeral undertaking, but his great interest was music. He wanted to make choral singing truly popular and, inspired by the Jubilee Singers from the United States, in 1901, he formed the Toynbee House Choir at 25 Rottenrow. He was self-taught as a choir master, but the new choir quickly gained something of a reputation after performing at the East End Industrial Exhibition in 1903.
A desire for greater independence led to a break from Toynbee House in 1906 and the reformation of the choir as the Glasgow Orpheus. Roberton himself composed and arranged many of the songs and part songs of the choir and it soon gained a national reputation. This became an international one after a triumphal tour of Canada and the United States in 1926. Selection for the choir was rigorous with voices assessed each year.
In 1914 he joined the Independent Labour Party and he and Mrs Roberton, both of whom were pacifists, gave support and hospitality to their close friend, the Labour leader Ramsay MacDonald, especially during the years of the First World War. Roberton was knighted in 1931, when MacDonald was prime minister, and he continued to lead the choir until 1951. With memorable arrangements of songs such as "All in the April Evening" and the 23rd Psalm, Roberton and the Orpheus inspired and encouraged the spread of choral singing throughout the country. On his resignation it was decided to disband the Orpheus and re-form it as the Glasgow Phoenix Choir.