Sunderland born centre forward Randolph Galloway started his football career with local junior club Sunderland Tramways in 1921 before joining Second Division Derby County in October 1922, making his Football League debut against Southampton that December. He soon established himself in their first eleven scoring twice in the return fixture a week later and Galloway was part of their FA Cup team that went all the way to the 1923 semi final only to be beaten 5-2 by West Ham United at Stamford Bridge.
In 1923-24 he netted 21 goals as Derby finished 3rd narrowly missing out on promotion, and he was signed by First Division Nottingham Forest in November 1924 after 30 goals in 76 appearances for The Rams. However in his first season Forest were relegated and Galloway moved on to Luton Town in June 1927 after 8 goals in 43 appearances for Forest. His stay at Kenilworth Road was a brief one, scoring once in 2 appearances in the late summer of 1927 before joining Coventry City in January 1928, where he scored on his debut but still only managed 4 appearances before the season end.
He joined Second Division Tottenham Hotspur in August 1928 and scored on each of his first two games that September, however his third game proved to be his final appearance (assumedly he was forced to retire from the professional game due to injury), and the following year he joined Midland League club Grantham Town.
He then embarked on an interesting overseas coaching career, spending six years in Spain between 1929 and 1935 where he coached Sporting de Gijón from 1929 to 1931, Valencia CF from 1931 to 1933 and Racing Santander from 1933 to 1935. After the Second World War he coached Costa Rica in 1946, then Uruguayan club Penarol in 1948, and Swiss team Sport Club Juventus from 1949 to 1950. He then spent five years in Portugal as manager of Sporting Lisbon from 1950 to 1953 and Vitoria Setubal from 1954 to 1955.