Am I a software artist? It would be fun to call myself that. Coding usually starts with a blank canvas (an empty text buffer) and I write not sequentially but through gradual refinement. Artists usually work in a similar way. The dictionary clearly supports the idea that software development could be called an art:

Art \Art\ ([aum]rt), n. [F. art, L. ars, artis, orig., skill in
 joining or fitting; prob. akin to E. arm, aristocrat,
 article.]
 1. The employment of means to accomplish some desired end;
    the adaptation of things in the natural world to the uses
    of life; the application of knowledge or power to
    practical purposes.

-- Webster's Revised Unabridged Dictionary (1913)

However, today's usage of the term connotes pleasing the senses. Software may have a beautiful structure, but that structure can only be appreciated by the mind, not directly by the senses. That distinction may require software to have a pleasing appearance before most people will call it art.

In reality, I think software development has elements of engineering, science, and art. Many software development tasks require all three mindsets. When I'm writing code, language syntax and patterns are engineering, profiling is a bit of science, and choosing the right name for things is definitely an art. When I'm building a user interface, getting the layout and interactions right is engineering, getting proper feedback is a science, and solving unusual user interface problems is an art.