[8] Parker, a fullback, began his career with Kello Rovers, turning semi-professional when he joined Falkirk in 1952.
The highlight of Parker's time with the Bairns was their 1957 Scottish Cup victory, as they defeated Kilmarnock in a replayed final.
[2] He eventually became a stalwart in the side which won the 1962–63 league championship, finishing six points ahead of runners-up Tottenham.
in December 1969 and made his League of Ireland debut at Tolka Park on 4 January 1970 in a 3–1 defeat to Dundalk.
[2] This also transpired to be his final national team cap, which some regarded as "perverse"; former teammate Alex Young stated that Parker was still the best player in his position in Britain.