In any canon series of Star Trek has a human been able to master the mind meld?
Miranda Jones joins minds with Ambassador Kollos in TOS: Is There in Truth no Beauty?
MIRANDA: Thank you, but the assignment's not yet definite. It will depend upon my ability to achieve a true mind-link with the Ambassador.
SPOCK: I'm sure you will find it a fascinating experience.
MIRANDA: I am one with Kollos.
She is an unusual human as she was born a telepath.
According to the novelization of Star Trek III: The Search for Spock, authored by Vonda N. McIntyre, Spock's mother had mastered the Vulcan mind melding skills. In the book, there are additional scenes on Vulcan, with Amanda Grayson as the viewpoint character. The scenes provide some additional background on Vulcan mysticism for the reader, and as part of the exposition, it is revealed that Amanda has gone through the Vulcan spiritual training and reached the level of competence that is normally required of Vulcans.
However, the canonicity of this material might be considered dubious. The books presents a subtly different description of the Vulcan mysticism than appears in the final movie. (These ideas may have originated with McIntyre, or they may have been from an earlier version of the film's treatment/script.) The character played by Judith Anderson is credited in the film as the "Vulcan High Priestess." However, in the book, her position does not seem to have any religious overtones, and by virtue of being the most skilled practitioner of the Vulcan mental arts, she was referred to simply as "the adept." (It is actually mentioned in the book that the current adept had actually recently stopped using that title, since she did not feel that it was right to set herself above all the other skilled Vulcans.) And, of course, there is the idea that a relatively normal human could expect to achieve Vulcan-level skills over the course of just living several decades on Vulcan.