Do an NGRAM search for such terms as “leftist” and “rightist” or “left deviationist” or “right deviationist” or “left winger” or “right winger”, etc. and it becomes crystal clear that the language of “left” and “right” come into the English language and American conversation in the 1920s and especially the 1930s.
Do a search of a host of the dominant intellectual magazines across American history at Unz.org and the first modern introduction of the language of “left wing” and “right wing” can be found in a 1919 Literary Digest article on the socialist parties in Russia. The battle over the statist and socialist program in Russia was fought between “left” factions and “right” factions, and when the Communist Party took over, the battle to control the part and the party line was fought in terms of “rightist” factions and programs and “leftist” factions and programs. Depending on who he was out to destroy, Stalin moved back and forth between factions, and ultimately labeled anyone he wanted to destroy as a “right deviationist”. Earlier Lenin had attacked “left wing communism”. Trotsky and the Trotskyites battled for the mantle of being the leftist “good guys”, while Stalin’s Comintern liked to label all rivals among the various statist and socialist campts as right wing “bad guys”.
Note that all of these battle were raging in Russia across the 1910s and 1920s and 1930s, but you don’t find don’t find this language used to characterize American political struggles and debate until this sort of language began to trickle in from Russian and the Russian socialists, anarchists and especially the Russian and Comintern communists and ex-Russian Trotskyites, etc.
Americans between 1789 and the 1930s did not characterize their political debates in terms of the Russian socialist and communist party labels of “left” and “right”, and this language only slowly trickled into American usage, very often coming out of the socialists and communist publications in New York and Chicago with surprisingly massive circulation figures.
I’ll add more and update later.
UPDATE: I find a writer for the British Labour Monthly as late as 1924 groping to make sense of how to use the words “left” and “right” in the British Labour Party context, and struggling to define who or what is “left wing” and what is “right wing” within the rival factions and programs of the British Labour Party and within the various socialist and statist parties on the Continent. When this author looks for examples to make sense of how to use the terms, he doesn’t refer to 18th century France and its Parliament, he refers to the positions and factional fights among socialists parties in Russia and in Germany in the midst of WWI, and to the Communist International and the German Socialist Party.