Is true that poisons can be made to target a single person using their DNA?

Theoretically, yes, it’s certainly possible. I must say, I haven’t heard of such a project, however it would by no means surprise me if at least governments had this in the works. As you could imagine, it would certainly be useful.
The mechanism by which this could occur are numerous, stating the use of DNA, as you have, is merely the tip of the iceberg. The RNA, introns and Ribosomal, aswell as mitochondrial, DNA fragments that could also be targeted make this a true possibility.
Though, as I have stated, I know of no such current projects. Most appear to be based on saving mankind, rather than destroying it :-P

No, this would be virtually impossible. All of the key components of cellular functionality are conserved from person to person (such as the enzymes involved in DNA synthesis, RNA synthesis, protein synthesis, etc.), and small polymorphisms (subtle differences in the DNA sequence) would be almost impossible to target.

I think I’m going to side with shilolo on this. Sounds like the plot from a sci-fi novel.

I know what I’m writing about this November. NaNoWriMo, here I come!

Which is, I guess, my way of saying that it sounds outrageous. But then again, a small machine the size of a wallet with all the information of the world at my fingertips would have sounded the same even 50 years ago.

The neocon Project for a New American Century posits the idea that “advanced forms of biological warfare that can ‘target’ specific genotypes may transform biological warfare from the realm of terror to a politically useful tool”.”

Poisons, as we commonly view the word, are not DNA specific chemicals. They are life-form specific.

Cancer research/treatment seems to be advancing in cell specific poisoning.

I wouldn’t ever claim that DNA specific poisoning isn’t possible, but much of our DNA is common, not only among humans, but between humans and other animals, so I’m not anxious about the prospect…unless you know something I don’t.

This is definitely a Star Trek: The Next Generation plot, perhaps used in other places as well. While I don’t think is impossible, its as unlikely as warp drive or a teleporter. It would quite hard to make a virus that checks for all the right genes of a person.

Hmmm… there is an idea floating around in medicine (or a hope) that we can use particulars of someone’s genetic code to create medicines particularly for them (i.e. no side effects for them personally, precisely modulated dosage, etc.). It seems like you could reverse the idea to target poisons. I don’t think you would develop a new chemical compound though. The simplest way would try to study someone’s DNA to see if there were some particular weakness or vulnerability (@jvgr: the DNA isn’t targeted, of course; it just tells you where a good spot to target might be). An obvious example: say you could tell from someone’s DNA that they were hyperallergic to peanuts—this suggests an easy way to poison them without hurting others. Now replace peanuts by any other known chemical, and you have your strategy.