Kilnhurst, Yorkshire born inside right Ralph Burkinshaw began his football career with Mexborough Town in 1913 and spent 1914-15 on the books of Barnsley without making a first team appearance for them. After the conclusion of the First World War he joined Second Division South Shields in August 1919 and made his Football League debut at Fulham in August 1919, playing once more for Shields in the return fixture a week later before joining non league Wath Athletic later the same year. In September 1920 he joined Northampton Town, but didn’t make their first team before joining Gainsborough Trinity in October 1920. This brought him to the attention of Second Division Bury who signed him on 17th November. His Bury debut followed ten days later in a 5-0 defeat at Barnsley, and he soon became a regular feature in the first team, helping them to win promotion to the top flight in 1923-24 as Second Division runners up.
After one season in the First Division, by when he was on the fringes of the Bury first team, he joined Bradford City in July 1925 having scored 20 goals in 108 appearances for The Shakers. He had five seasons at Valley Parade, and although they were relegated in his second season, he was an ever present as they won the Third Division (North) Championship in 1928-29, by when he had moved to right half. After a single season back in the Second Division he transferred to Wrexham in July 1930 having scored 32 goals in 178 appearances for The Bantams. In his first season at The Racecourse they finished third in the Third Division (North), but when Jack Baynes was dismissed he became caretaker manager of the club for 16 matches from October 1931 to January 1932 until the appointment of Ernie Blackburn.
He scored once in 69 appearances for Wrexham before joining Midland League Scarborough in 1932, re-joining Mexborough in 1933 before finishing his career at Denaby United, whom he joined in 1936.
He was the younger brother of footballers Jack and Laurie Burkinshaw, who both had successful careers either side of the First World War, Jack playing for among others Swindon Town, where he won the Southern League, Sheffield Wednesday and Bradford Park Avenue, Laurie for Sheffield Wednesday, Birmingham and Halifax Town.