I don't see "Akashic" or "record" in the linked "Glossary of Buddhism" ... so the term "Akashic" might be Theosophist and/or from a tradition other than Buddhist, but I don't know.
Buddhism does believe in "Kamma" which I suppose is a way of saying that "events and experiences are stored".
The Wikipedia article references a 19th century book titled "Esoteric Buddhism" which says,
Early Buddhism, then, clearly held to a permanency of records in the Akasa, and the potential capacity of man to read the same when he has evoluted to the stage of true individual enlightenment.
There is something similar to that described in, for example, the Kevatta (Kevaddha) Sutta (in which the Buddha is someone who "evoluted to the stage of true individual enlightenment"), which says towards the end,
Recollection of Past Lives
"With his mind thus ... he directs and inclines it to knowledge of the recollection of past lives (lit: previous homes). He recollects his manifold past lives, i.e., one birth, two births, three births, four, ... , many aeons of cosmic contraction and expansion, [recollecting], 'There I had such a name, belonged to such a clan, had such an appearance. Such was my food, such my experience of pleasure and pain, such the end of my life. Passing away from that state, I re-arose there. There too I had such a name, belonged to such a clan, had such an appearance. Such was my food, such my experience of pleasure and pain, such the end of my life. Passing away from that state, I re-arose here.' Thus he recollects his manifold past lives in their modes and details. Just as if a man were to go from his home village to another village, and then from that village to yet another village, ...
That's part of the "miracle of instruction" (i.e. it's a miracle and instructive). Towards the top of that same sutta, the Buddha says,
Kevatta, there are these three miracles that I have declared, having directly known and realized them for myself. Which three? The miracle of psychic power, the miracle of telepathy, and the miracle of instruction.
That is somewhat quoting out of context, though.
It would be better to at least read the whole sutta than only the paragraph I quoted above, and to understand why the Buddha would call it "instructive" i.e. what he is trying to teach.