deoxyribonucleic ACID?
 

Why is DNA called an acid, when infact in it there is a base (adenine, guanine,thymine,cytosine)?

DNA is a nucleic acid, and as you stated is based from adenine, guanine, cytosine, and thymine which are not bases but rather sugars.

The comment above is incorrect. DNA consists of a backbone of phosphate and deoxyribose (a sugar). Nitrogenous bases connect the two. The term base is not used in the literal chemical sense (some bases act as bases, some act as acids). Intact nucleic acids are capable of donating hydrogen protons, hence they behave as weak acids.