No he didn't. He borrowed it from this guy:
Johann Friedrich Blumenbach - Wikipedia
And then they had a godawful row about it all. Blumenbach was a "monogenist" and an abolitionist (he collected literature and art produced by African slaves as a means of supporting his argument for they equality with white people) , who proposed the "Caucasian" (inhabitants of the Caucasus) to be the most esthetically pleasing of the white, European "variety" of mankind, and the whites to be the most beautiful variety. But he specifically rejected the idea that there were any differences in intellect or morality between any group of humans – humanity being a single species. (Blumenbach, a medical doctor and professor of anatomy by training, in other aspects was an extremely important and infleuntial theoretician, inventor of the important concept of "Bildungstrieb" fx.)
Meiners otoh wrote an entire book on the foundational concept that there were the beautiful "Caucasian", white, people who had created everything of any use – and the ugly, useless everyone one else.
Blumenbach was very cross over Meiners not just lifting the concept, but reconfiguring it like that. Blumenbach was also supported in the argument by the mathematician Lichtenberg and the natural historians father and son Forster, who had travelled with Captain Cook in the Pacific. They argued Meiners down to the extent that he shut up about the question of race until sometime in the 1810's when he clearly that the defeat of Napoleon had vindicated his views – that the defeat of the egalitarianism of the French Revolution was confirmation that his opponents back in the 1780's hade been wrong all along.
The funny thing about Meiners concept of history is that while he was inveterately racist, at least he assigned a role to non-Europeans in world history – unfortunately a purely negative one. (Later the Prussian school of history and source criticism founded by Leopold von Ranke solved the "problem" of non-Europeans by just writing them off as not having "real" written history, unlike the Europeans, and so they could be safely ignored. Various 19th c. schools of anthropology would however continue to think about non-Europeans and how they might related to Europe, the neo-Herbartian psyschologists (in philosophy) in Germany not least.)
Exactly why the United States got itself hooked on Blumebach's nomemclature of "Caucasians" is of these weird contingencies in intellectual history. Though we can assume England was involved in the transit – since both Blumenbach and Meiners (professor of hostory) were academics at the University of Göttingen, in Hannover, and so that important German annex of the Hannoverian kings of England. Göttingen was a vector for transiting a lot of important German science to Britian.