Huh? Really?
Yes.
The term soccer is a shortened form of assoccer, which is itself a shortened form of association football. The abbreviations came from the English schoolboy tradition of taking the name of something (say rugby), chopping off all but the first few syllables and appending "-er" or "-ers"; hence "rugby" became "ruggers" and "association football" became "assoccer" or, eventually, "soccer". The term is used in just about every English-speaking country that isn't England in order to distinguish the sport from other forms of football like the two rugby codes, the two gridiron codes, or Australian Rules.
(As for those being called football even though the ball is typically being carried in the arms or hands, the term comes from the need to distinguish such sports, which were played on foot, from those like polo played on horseback.)