I have seen a couple of Turing's papers, but never have found one called "The Imitation Game". The Imitation Game seems to be a name used by Turing to refer to his test to decide whether an intelligent entity of some sorts is machine or man (a.k.a., the Turing's test). But I haven't found any published paper with that name. So, did Turing ever publish a paper called The Imitation Game?
No but also yes. In the 1950 edition of "Mind", Turing published "Computing Machinery and Intelligence" (doi: 10.1093/mind/LIX.236.433, JSTOR, text, PDF) on the subject of artificial intelligence. Wikipedia has a good overview of the article and its implications; however, if you refer to the article itself you will note that the first section is titled "The Imitation Game",
1. The Imitation Game
I propose to consider the question, "Can machines think?" This should begin with definitions of the meaning of the terms "machine" and "think." The definitions might be framed so as to reflect so far as possible the normal use of the words, but this attitude is dangerous, If the meaning of the words "machine" and "think" are to be found by examining how they are commonly used it is difficult to escape the conclusion that the meaning and the answer to the question, "Can machines think?" is to be sought in a statistical survey such as a Gallup poll. But this is absurd. Instead of attempting such a definition I shall replace the question by another, which is closely related to it and is expressed in relatively unambiguous words.
So while it was not the title of the paper, it was used as a section title in the paper.