I have convinced myself that this quote is not by Alan Turing, much of this is indebted to kimchi lover's leads. The main issue here is that summary characterizations and paraphrases are misread as quotations, and the form in which the summary characterization is given does not strongly proclude that reading. Let me go through the evidence.
Turing does not have a categorical but a dynamic-behavior notion of intelligence. Most importantly intelligence is not just about being right, but being in error in interesting ways (for both machines and humans).
This has been variable demonstrated by numerous close readers of his work. See:
But of course his own, rather intriguing writing. I recommend his posthumous lecture/article:
There would be plenty to do in trying, say, to keep one's intelligence
up to the standard set by the machines, for it seems probable that
once the machine thinking method had started, it would not take long
to outstrip our feeble powers.
Other passages in this article suggest a dynamic notion of intelligence. If I'm permitted a commentary, we don't say about humans: you are intelligent or not, and Turing's discussions on comparing include an awareness that this is not how it works. Consider this passage:
My contention is that machines can be constructed which will simulate
the behaviour of the human mind very closely. They will make mistakes
at times, and at times they may make new and very interesting
statements, and on the whole the output of them will be worth
attention to the same sort of extent as the output of a human mind.
In short Turing's arguments include arguments about the output of the human mind and how it can make mistakes and say something new and interesting.
Turing does not view the imitation game as a game of deception. A search of his collected works Vol 1 Mechanical Intelligence reveals the use of the words "deceiving" only once and no matches for "deceive" "deceit" or "deception". But that one use is interesting:
Among the first and most famous was the chess-playing automaton
constructed in 1769 by the Baron Kempelen; M. Maelzel took it on tour
all over the world, deceiving thousands of people into thinking that
it played the game automatically.
So Turing does start of his consideration with an example of deceptive imitation, here of humans pretending to be a smart machine. However, this "deception" framing is absent from any of his other discourse and specifically from his detailed discussions of the imitation game. However, it might explain the deception reading of Turing later.
Hodges uses the following sentence (Hodges, A. (2014). Alan Turing: The Enigma):
It was no new idea, therefore, when Alan talked in terms of an
imitation principle: that if a machine appeared to be doing as well as
a human being, then it was doing as well as a human being.
Notice that this form too might allow the careless reader to see the part after the colon as potentially an Alan Turing quote, rather than a characterization of his ideas.
But Hodges' writing is noteworthy also for how he describes the imitation game human on human example of Turing:
He imagined a game in which an interrogator would have to decide, on
the basis of written replies alone, which of two people in another
room was a man and which a woman. The man was to deceive the
interrogator, and the woman to convince the interrogator, so they
would alike be making claims such as ‘I am the woman, don’t listen to
him!’
This characterization does not appear in Turing. In general deception is an important theme in Hodges book, leading to a strengthened "imitation as deception" reading not explicitly found in Turing.
As noted, kimchi lover has excavated some very good leads. Indeed I believe that the Introduction by Shannon and McCarthy is a likely source for the formation of the quote text. It reads (as reproduced in Copeland, B. Jack, (2004) The Essential Turing. Clarendon Press):
One interesting definition has been proposed by A. M. Turing: a machine
is termed capable of thinking if it can, under certain prescribed
conditions, imitate a human being by answering questions sufficiently
well to deceive a human questioner for a reasonable period of time.
A worthwhile point to be made about this wording is that while suggestive of a quotation, it could well be a summary and/or a paraphrase. The quote in question can be viewed of a further compactification of the Shannon/McCarthy sentence, but dropping parentheticals, and sharpening the wording.
As a side-note, Feigenbaum and Feldman (1963) Computers And Thought, McGraw-Hill has been mentioned. In their introduction (p.3) we find the following:
What, then, is the goal of artificial intelligence research? As we
interpret the field, it is this: to construct computer programs which
exhibit behavior that we call "intelligent behavior" when we observe
it in human beings.
This does appear to have at least some structure of the quote in question, and while following discussion of Turing's notions it is not attributed to Turing.
How precisely the transition from all these lines to the quote was made is a bit unclear. I do believe that kimchi lover's lead to Person, Graesser et al is a good one. Indeed in their (2002) paper one finds:
According to Turing, a computer could be described as intelligent if
it could deceive a human into believing that it was human.
It is important to notice that this too can be read either as a quote, or as a paraphrase/summary and it is quite plausible that it was lifted from here as if it was indeed a quote. (Note: Google books gives an earlier hit at 1997, but given that the quoted text is identical to the 2002 source above I would wager that it's a misrecognition by google books).
To recap, the quote in question is:
A computer would deserve to be called intelligent if it could deceive a human into believing that it was human.
Notice that this is a slightly strengthened rewording of Person, Graesser et al. "could be described as" becomes "would deserve to be called".
Now this is not proof positive of the evolution. It could be that Person, Graesser et al were inspired by the given quote. However, I find this unlikely given that their quote is closer in the spirit of Turing than the quote now spread over popular quotation sites.
There are famous misquotations born like this. A well-known example is Evelyn Beatrice Hall attributing an attitude to Voltaire, that then survived as a false quotation of Voltaire. In other words the confusability of loosely written paraphrases are potential sources of misquotations.
So to summarize, there is a history of summary descriptions of the Turing test, that are sometimes but not always presented in a way that a careless reader can think of them as direct quotes.
P.S. All italics are mine for emphasis.