Writing is no less an art than painting. Anyone can write the same way anyone can draw, but if you put a paintbrush in a man's hand, he probably can't paint the Mona Lisa, and in the same way, if you put a pen in his hand, he probably can't write a best-selling novel, or even a good plot for one. It's an art that takes years of hard work to learn and go anywhere with. I don't see why this is even a question, and even before I was an author myself, I never could understand why it is.
Despite the resounding opinion of the majority here, I'd like to play Devil's Advocate and mention that not all establish writers even consider what they do 'art'. I just watched a recorded seminar featuring John Irving and he called himself a 'craftsman' much like an architect. Though imagination is key, he placed importance on the structure of the whole, not on the creative 'what-ifs' and 'maybes'. He stressed knowing the end first, and not just the general idea, the actual words, so that you can establish repeated lines and themes. He doesn't even begin to write until he knows the story. In this way, he is just relaying a tale he already knows unto paper when he begins, only having to focus on the physical structure of the sentences and the whens and hows the information is revealed to the readers.
Personally, I do believe it is art. It just requires greater construct than a visual media. As the saying goes "A picture is worth a thousand words".
I don't even mean that in a snarky "bad writing doesn't count" sort of way. It's just a fact: some people are illiterate. This becomes even more of a point to consider when you realise that, in order to write, you first have to master (or at least become proficient in) the language. I consider myself a competent writer in English, but that's not going to help me write a book in Italian. And it's only comparatively recently that even most people have become able to write in their own language.
Which do you reckon you'd do better at: writing a novel in Russian or making a sculpture out of marble? I'll bet your sculpture would look more professional today than your novel would look in two years.
That said, I usually consider "art" to mean visual art. The sort of thing you would see in an art gallery. I don't go into a bookshop to "buy some art."
1. The expression or application of human creative skill and imagination, typically in a visual form such as painting or sculpture,...: "the art of the Renaissance" 2. Works produced by such skill and imagination.
This seems to come from the Oxford Dictionary. That dictionary also includes: 4. a skill at doing a specified thing, typically one acquired through practice: the art of conversation
Writing fits both of those definitions. As pretentious as we might like to be and despite all the wank about what "art" is, I choose to see art is relatively easy to define. We can have much more worthwhile bohemian circle jerks on what makes are good or bad but as for what art IS, well, that's easy.