Who invented DNA?

The correct answer to your question would be GOD invented DNA, however if by invented you imply "Who discovered DNA ?" here is the answer -

Albrecht Kossel was the German Scientist who first isolated,identified and Named DNA as we know it today. He was the first to identify the four building blocks of DNA adenine (A), cytosine (C), guanine (G), thymine (T). He was awarded Nobel Prize in 1910 for his work.

As per popular belief it was not Watson & Crick who discovered DNA their contribution was Double Helix Model of DNA. They received a Nobel in 1962 for Watson & Crick Model of DNA not for the discovery of DNA.