I believe that the term is an abbreviation. When the various forms of football were consolidating in Britain during the 1800's there were two bodies created the Rugby Football Union and the Football Association.
With the English propensity for reducing names the Rugby Football Union game became Rugby, later splitting into amateur Union and Professional League camps. These are the men who play with the funny shaped ball. :) Later American Football adopted many of their rules from this game.
The Football Association game was then called soccer from the reduction of the word association. Now commonly known as some variant of the word football around the world, but to Americans known as soccer.
So no, soccer is an English word not American in origin