RaceYouAnytime's first recorded occurrence from 1952 will be very difficult to beat, and the fact that the first occurrence is in a newspaper dedicated to a black readership strongly suggests an African American origin of the term.
I have a handful of additional data to offer in support of RaceYouAnytime's answer. First, Charles Doyle, Wolfgang Mieder, and Fred Shapiro, The [Yale] Dictionary of Modern Proverbs ((2012) has this fairly lengthy entry for the expression:
What goes around comes around.
1961 Proceedings of the Fourteenth Biennial Convention of the International Longshoremen's and Warehousemen's Union 242: "The need has always been for the Negro to be a full part of the Labor Movement, and I don't think you can deny him this right. And if you do, you are taking away the rights belonging to you, because the old saying goes, 'What goes around comes around.'" 1962 Paul Crump, Burn, Killer Burn! (Chicago: Johnson) 132: "'Yeah,' he sneered, 'I'll hang tough. Only you guys remember—What goes around, comes around.'" Gregory Titelman,]R[andom] H[ouse] D[ictionary of America's Popular] P[roverbs and Sayings (2000)] 355–56; [George Bryan & Wolfgang Mieder,] [A] D[ictionary of] A[nglo-]A[merican] P[roverbs & Proverbial Phrases Found in Literary Sources of the Nineteenth and Twentieth Centuries (2005)] 831; [Fred Shapiro,] Y[ale] B[ook of] Q[uotations] Modern Proverbs [(2006)] (37); [Jennifer Speake,] [The] O[xford] Dictionary of] P[roverbs], fifth edition (2008) 134–35; [other citations omitted]. Also occurring is a variant (or counter-proverb?—but the meaning seems to be the same): "What comes around, goes around." 1974 Title of a "soul" song by Dr. John: "What Comes Around (Goes Around)." 1983 Karen Payne, Between Ourselves: Letters between Mothers and Daughters (Boston: Houghton Mifflin) 267 (in a letter dated 1 Dec. 1980): "It seemed significant, having lost three friends that past winter, that three new lives would enter the valley next winter. What comes around, goes around, right?"
Geneva Smitherman, Black Talk: Words and Phrases from the Hood to the Amen Corner (1994) has no doubt that the expression is of African American origin:
WHAT GO ROUND COME ROUND
A proverb that expresses perhaps the essence of traditional "root culture" Blacks' belief about life, that whatever has happened before will occur again, even if in a different form. In a study of over a thousand proverbs used by African Americans, this was found to be the most frequently used proverb in the African American community (study conducted by Jack L. Daniel, Geneva Smitherman-Donaldson, and Milford Jeremiah, reported in "'Makin a Way Outa No Way': The Proverb Tradition in the Black Experience, Journal of Black Studies, June 1987).
In an Elephind search, the earliest match for the expression is from 1966 in another primarily black-focused newspaper. From William Alexander, "Time for Talk," in the Indianapolis [Indiana] Recorder (July 23, 1966):
I had the occasion to run into Attorney Robert G. Mann at Scotty's Lounge and he was very adept at making funny remarks concerning the "Muhammad Speaks" Newspaper. I had just purchased one to read and he asked me to see it. I showed it to him and he remarked to Gary Jones and City Prosecutor Taylor Baker, along with others, this is the weekly edition of The Recorder. I remarked that is about the size of it. I feel that any person is entitled to purchase anything that he so chooses, if he has the money to pay for it. What a smug look he had on his face then. Well what goes around comes around, right, Robert G.
An interesting bit of evidence that the expression was not well known in the broader U.S. culture as late as the middle 1970s involves an evident typo in aquotation. From Decisions and Orders of the National Labor Relations Board (1974): [combined snippets]:
In November 1970, Jackson returned, again for Jervier's signature on the "new contract," this time also presenting to and asking Jervier to sign a paper deauthorizing GRAMC to act as his bargaining agent. After a telephone conversation with a GRAMC official, in the presence of Jackson, Jervier refused to sign either the deauthorization slip or the contract. Jackson warned him, "There is no win and what does around, comes around . . . . [You're] not doing [your]self any good for not signing." Soon thereafter (December 9, l970)——still in the context of continuing refusal by Jervier to heed Jackson's demands to sign a "new contract" with Local 705—Jervier instructed his employee, Reed, to supply customers with dimes at their request when needed for the use of the restroom; but Reed refused. Later, when a woman—apparently a regular caller—telephoned Reed again and Jervier asked her not to call so often, Reed called Jervier a "dirty black f—er."
In this account, Jackson's race is not identified, but Jervier is black. It seems likely that both Jackson and Jervier were familiar with the expression "what goes around comes around," but the person proofreading the NLRB decisions evidently was not.
Finally, Lewis King, Vernon Dixon & Wade Nobles, African Philosophy: Assumption & Paradigms for Research on Black Persons (1976) has this to say about the expression:
This point is well demonstrated by one of our more common proverbs. The Black child who is told that "what goes around comes around" may be receiving a specific admonition with regard to the consequences of his behavior, but he is simultaneously experiencing a reinforcement of the African world view, namely, that there are vital connections among events and experiences. Both the specific admonition and the general philosophical perspective are synthesized in the child's developing conception of the world. ...
It is no accident, then, that "what goes around comes around" is a common African-American proverb. As suggested above, the concept of continuity between events and experiences that is so fundamental to the African world view is clearly expressed here.