Does anyone use 'normalcy'? It is ridiculed in Britain as an American affectation, especially since there is a time-honoured word which means exactly the same thing i.e 'normality'.
The OED lists normalcy as a headword with "Chiefly U.S." There is a telling citation:
1929 G. N. Clark in S.P.E. Tract xxxiii. 417 If..‘normalcy’ is ever to become an accepted word it will presumably be because the late President Harding did not know any better.
The earliest citations are from 1845, in a strictly mathematical sense (the condition of a line being normal [perpendicular] to another).
Normality dates from a similar time, but has the sense of "what may be usually expected". British English has retained that distinction.
Nothing to be ridiculed about as such.
Although sometimes used, normalcy is less common than normality in American English. It is very rarely used in the UK, Canada, Australia, and New Zealand. It is frequent in India, however. (Wiktionary)
The word normalcy is used both in AmE as well as BrE, though to a lesser extent than normality.
normalcy vs. normality, AmE, 1900-2009
normalcy vs. normality, BrE, 1900-2009
Overall, normalcy seems to be used chiefly in news reporting and commonly in its 'idiomatic' sense (see further below).
normalcy vs. normality, English, 1900-2000
The American tendency for normalcy is probably based on its 'idiomatic' sense:
"A return to normalcy" (i.e. a return to the way of life before World War I) was United States presidential candidate Warren G. Harding’s campaign promise in the election of 1920. Although detractors believed that the word was a neologism as well as a malapropism coined by Harding (as opposed to the more accepted term normality), there was contemporary discussion and evidence found that normalcy had been listed in dictionaries as far back as 1857. (WP)