From Wiki “Conspiracy theory”/ origin and usage:
It cites a 1909 article in The American Historical Review as the earliest usage example,[45][46] although it also appeared in print for several decades before.[47]
The earliest known usage was by the American author Charles Astor Bristed, in a letter to the editor published in The New York Times on January 11, 1863.[48] He used it to refer to claims that British aristocrats were intentionally weakening the United States during the American Civil War in order to advance their financial interests.