In Google Search results across the period 1700–2008, the (not very numerous) matches for "accepted to join" are surprisingly heavily skewed—t least in the period before 1990—toward instances from Kenya, suggesting that the phrase may be an established idiom in that country.
The earliest match for the phrase, however, is a single-sentence paragraph a letter from George Washington to General William Heath, dated June 2, 1782, in The Writings of George Washington from the Original Manuscript Sources (1939):
The Soldier Gilbert may be accepted to join his Regiment.
This instance, besides being an outlier chronologically, is unusual in being couched in passive voice. The next match is from The Golden Key, Proving an Internal Spiritual Sense to the Holy Word (1817):
After the Lecture we repaired to the residence of the before mentioned Susanna, and were regaled with a pleasant repast, consisting of all the delicacies of the season, for Susanna's affection for the intended bride was ardent; we also were much refreshed in the splendid baths, fitting us for further exercise of mind and body, which presently became fully employed, as it was proposed and accepted, to join the gay throng, whose graceful ambulation while passing, had some time engaged our attention.
The next four matches begin almost 150 years later—and all four are from Kenya. From Constitutional Advance (June 14, 1961) in Colony and Protectorate of Kenya: Legislative Council Debates, first session (1961):
The Minister for Commerce, Industry and Communications (Mr. Muliro): ... Some hon. Members also argue, "Don't worry about anything else". The hon. Members who have accepted to join the Government have done something wrong. We should rather let the country sink back into chaos, poverty, ignorance and misery in order to get any place. I wonder ho many Africans in this country would be delighted to see Kenya going to economic chaos and ruin?
From Second Reading of the Electric Power (Amendment) Bill (March 3, 1965), in Kenya National Assembly Official Record, volume 4 (1965):
Mr. Gichoya: ... Every single person, Mr. Speaker, did anticipate a change when Kanu came into power, when Kadu accepted to join Kanu, and that change was not just a mere political change or amalgamation by putting the two parties together, but it was meant that that Kadu had accepted the Kanu manifesto, which says that we are going to adhere to socialism.
From Question No. 991 ("House Allowance for Machako Hospital Employees") (November 20, 1970) in Kenya National Assembly Official Record, volume 21 (1970):
Dr. Munene: ... For example in a question like this, if there is a reduction, on a legal matter, as the Assistant Minister says, he should tell us, "Yes, we reduced it." for somebody who has accepted to join the Government scale or to go out into the field. He should know exactly what is happening—
The Speaker (Mr. Mati): Order! Dr. Munene, you are just making a speech.
From Question No. 594 ("Employer Contribution to National Hospital Insurance Fund") (June 30, 1981), in Kenya National Assembly Official Record, volume 55 (1981):
Mr. Abuya Abuya: Mr. Speaker, Sir, can the Assistant Minister confirm or deny that those people who are earning less than Sh. 1,000 and those people who are not employed are not accepted to join the scheme as from 1978?
The string of matches from Kenya is finally broken by this match from Proceedings of the Fourth ACM SIGACT-SIGMOD Symposium on Principles of Database Systems, March 25-27, 1985, Portland, Oregon (1985) [snippet not visible in viewing window]:
Hence, at the end of the second phase, only a subset of the processors in A might actually be assigned to the virtual partition v they have accepted to join at an earlier moment.
Google Books matches from more-recent years show much wider adoption of the wording—31 matches in published (and presumably edited) books between 2001 and 2008, but the phrase "accepted to join" is surely less common than either "agreed to join" or "accepted membership in [or a position with or something similar]."
In my view, the problem with "accepted to join" isn't a matter of grammaticality but of idiomatic familiarity. I wouldn't use it, but I can't say that I find its intended meaning difficult to unravel.