The simple answer to your question is no. The technology to do such a thing doesn't exist as yet and may never do.
Since this is WB then it is possible to conceive of WB scenarios where it can happen? Absolutely yes. Its a fairly widespread trope of Sci-Fi that's been explored by a number of authors ranging from Ken MacLeod (Fall Revolution series) and Peter Watts (Firefall). Also present in film such as the Matrix Trilogy where Agent Smith takes over a human body.
One key thing for you to think about is whether you are thinking primarily about DNA modification or memory modification as they are very different things.
One is modifying the existing structure of the brain (its software) the other is modifying the blueprint for how a human is built (its hardware schematic).
Ken Macleod and the matrix covers the former - AI's altering/overwriting our brains like a computer virus in various ways ranging from accessing pre-existing radio implants or direct re-writing via the optic nerve.
Peter Watts approach combines both the former and hints at the latter. The latter hints at a phenomenon called emergent complexity - essentially developing complex constructions (in this case a human/AI hybrid) from simpler structures - in this case DNA. Peter Watt's approach describes an alien doing this - but we could use the same approach for an AI - as by definition they are an alien and possibly more superior lifeform. Taking this approach its conceivable using some kind of Hand-wavium that an AI for some reason might chose to create a human embryo with its DNA pre-encoded to generate a copy/facsimile of itself.
How/Why it would do this rather than just taking over a pre-existing human would be an additional exercise for your world building/plotting.
If you go down this route you will probably want to do some reading about the differences between the human genome and the human proteome.