Best I can tell, the term originated in agency law regarding the doctrine of Respondeat Superior (whether the person who hired the individual was responsible for that individual's actions). Essentially, masters were culpable for the actions of their servants, but not for those who were independent and not subjected to direct supervision.

I looked at cases prior to 1900 in Massachusetts, New York, and Pennsylvania. The difficulty I'm having is all these cases start around 1870-1890, but they use the term pretty much as accepted law. It makes it difficult to pin down its original use. The earliest case I found that used the term was in Pennsylvania in 1841. However, there are other cases that use similar language without the word "contractor," so the concept is likely older. It's also possible that the cases simply aren't widely available online that go back farther with that term.

It is not an American innovation. The exception that proves the rule (as the term is properly used) is Honeywill and Stein Ltd v Larkin Brothers Ltd, 1 KB 191 (1934), which created liability for employers of independent contractors engaged in extra-hazardous activities. Sadly, my access to English cases are far more limited than American cases, so I can't really elaborate.