mid-14c., “a plotting of evil, unlawful design; a combination of persons for an evil purpose,” from Anglo-French conspiracie, Old French conspiracie “conspiracy, plot,” from Latin conspirationem (nominative conspiratio) “agreement, union, unanimity,” noun of action from past-participle stem of conspirare “to agree, unite, plot,” literally “to breathe together” (see conspire).

Earlier in same sense was conspiration (early 14c.), from French conspiration (13c.), from Latin conspirationem. An Old English word for it was facengecwis.

Conspiracy theory “explanation of an event or situation involving unwarranted belief that it is caused by a conspiracy among powerful forces” emerged in mid-20c. (by 1937) and figures in the writings of, or about, Charles Beard, Hofstadter, Veblen, etc., but the degree of paranoia and unreasonableness implied in each use is not always easy to discern. The phrase was used from 19c. in a non-pejorative sense “the theory that a (certain) conspiracy exists,” especially in court cases. Its use in general reference to theories of hidden cabals pulling wires behind the scenes of national or global events is by 1871.

We shall better understand the ensuing civil war if we study the movements in the four most important of these States, in relation to a theory which asserts that the secession was a conspiracy whose central cabal, composed of Southern senators and representatives in Washington, dictated through its ramifications in the States the inception and the course of the revolution. [James Ford Rhodes, page headed “The Conspiracy Theory” in “History of the United States from the Compromise of 1850,” New York, 1893]

To the Jingo Imperialist “the South African Conspiracy” is the alleged Dutch conspiracy to drive the British into the sea. But, to the man accustomed to weigh evidence and to base his opinions on ascertained facts, it is clear that this conspiracy theory is absolutely untenable, for whatever “evidence” has been adduced in support of the theory is nebulous and shadowy in the extreme. [“The South African Conspiracy,” in “The Westminster Review,” January 1902]

https://www.etymonline.com/word/conspiracy