Hey I thought I would upload a picture to help clarify what Davescat said (that sounds funny).
At the ends you will see a cyclic structure (ddeoxy ribose) with PO3? 4 on the tops. That PO3?4 is what makes it acidic! If you have questions like this again you should look at the functional groups of molecules because it will help you when you take a class like biochem (you have to memorize most of the functional groups like C=O and PO3?4) http://www.scientificpsychic.com/fitness/dna0.gif
DNA and RNA are considered acids since acids are protons donors or election acceptor. Acids are compounds that lose protons and RNA and DNA have phosphate atoms that make up part of the sugar backbone which take up electrons and are negatively charged.