Centre forward Geordie Henderson was born in Forfar, Angus, and began his professional career with hometown club Forfar Athletic in 1918, having joined them from local junior club Forfar Celtic. In 1919 he played briefly with Dundee before joining Glasgow Rangers in November 1919. His League debut with Rangers came in a Scottish League match against Aberdeen on 20th March 1920 and his first goal came a fortnight later on 3rd April against Airdrieonians. Henderson was top scorer at Rangers for four consecutive seasons from 1921-22 until 1924-25, the latter season being his most productive, netting 32 times.
He played a total of 195 League and Cup matches for Rangers and scored 141 goals. During his eight year spell at Rangers he amassed four Scottish League Championships in 1921, 1923, 1924 and 1925, as well as four Glasgow Cups and two Charity Cups. Although he did not represent Scotland, he played once for The Scottish League scoring in a 1-0 win over The Irish League in October 1923.
He left Rangers to join Second Division club Darlington for £2,250 in January 1927, where he made his Football League debut against Blackpool in February, making 14 appearances and scoring six goals as Darlington ended the season in 21st place and were relegated to the Third Division (North). In the autumn of 1927, he left Britain and signed with the New York Nationals of the nascent American Soccer League.
The Nationals finished third in league play, but won the 1928 National Challenge Cup in a two-game final against the Bricklayers and Masons F.C. of Chicago. The first game ended in a 1-1 tie after extra time, but the Nationals, on the strength of two Henderson goals, won the replay 3-0. In 1928, Henderson returned to Scotland where he signed with Dundee United. He spent only two seasons there, scoring 25 goals in 77 appearances, winning the 1928-29 Second Division Championship, before joining Welsh club Rhyl in the Birmingham & District League as player-coach in 1930.