Rock of Ages cleft for thee what does cleft mean?

"Cleft" is a variant of the Old English word "cleave" meaning to adhere, cling, or be faithful to something. Because of the song's verse "Nothing in my hand I bring, simply to the cross I cling," this could be its meaning.

"cleave" can also mean split, divide, separate.
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The above two responses are wonderful, and demonstrate that the word "cleft" or "cleave" is a famous example of what is casually called a "Janus" word. Janus was the Roman god of doorways, and of comings and goings. He was represented as having two faces, one on the front and one on the back of his head. The upshot is that a "Janus" word is a word that also means its opposite. There are many such words. Cleave, as in 'cleaver', means to split, divide or separate, and yet a husband and wife ideally 'cleave', or adhere, to one another.

I think the word in the context of the gospel hymn probably means 'cut', in the sense that a stonecutter would cut and dress a cornerstone for use. The line is "cleft for thee", and not "cleft to" anything.

While cleave is one of the best known Janus words, my dictionary suggests to me that cleft, a past tense, is usually connected with the "split or divide by a cutting blow" meaning. Cleaved is usually used in the context of adhering loyally.