I don't know that we have evidence to indicate that Jane Austen did consider herself an artist. There is nothing in her letters that indicates a reference to herself in a capacity as artist. However, she does make one or two facetious remarks and some of her critics speak of her in terms used for artists.
In one instance, Jane Austen says in a letter to her sister Cassandra (dated Saturday, November 17, 1798) that "Perhaps it would have suited [George] as well had [Jane's plans] been less elaborately finished; but an artist cannot do anything slovenly." In this statement, she is referring to designs she has planned for her brother George and not to her work as a novelist, and she is laughing at herself. She speaks in an ironical tone, poking fun at herself for probably going overboard in fulfilling George's request.
In the other instance, Jane Austen is responding to her nephew Edward who seems to have lost two and a half chapters of a manuscript of his own. Jane facetiously defends herself against the improbable possibility of a theft by saying: "What should I do with your strong, manly, spirited Sketches, full of Variety and Glow? -- How could I join them on to the little bit (two Inches wide) of Ivory on which I work with so fine a Brush, as produces little effect after much labour?"
Her most well-known and favorable critic was Sir Walter Scott. In one instance he says that Jane Austen's genius may not be the "highest" but it is certainly the "rarest." In his 1816 review of Emma, Scott says Austen gives "a correct and striking representation of that which is daily taking place." Later in an 1846 journal entry, after a third reading of Pride and Prejudice, Scott writes of Austen:
"...finely written novel of Pride and Prejudice. That young lady had a talent for describing the involvement and feelings and characters of ordinary life which is to me the most wonderful I ever met with...."
While the critical remarks about Jane Austen's novels never give a direct description of her as an "artist" (that is a more current phrase usage for literary authors), Scott's remarks show an indirect reference to her as an artist by discussing her "genius" and "talent." Whether her critics liked her work or disliked her work, the supporting reasons were the same.
The supporting reasons given by Austen's critics for their opinions were that she accurately saw and described the realities of life in the sphere of the commonalities of everyday life of people in Austen's class living in small villages, bearing in mind that Austen's class was educated (e.g., clergymen) and aristocratic (e.g., Knightly) and mingled with the nobel (e.g., Darcy); she described feelings and character of individuals; she described with accuracy how men should "act toward women and how women should act toward men"; she has characters who are good and those who are full of "folly" upon which the good ones have their virtues sharpened. There is much about the genre of early novels that Jane Austen stayed far away from (no damsels in distress, no abandoned babies and confused identities) but what she chose to do, she did "perfectly" and was "faultless" and a "great novelist," as stated by novelist Anthony Trollope in 1870.
For more information, read the many resources available from Jane Austen's Art and her Literary Reputation.
Jane Austen, S.E. Hinton, Harper Lee, Truman Capote and many other authors are artists; if you are an art artist like Georgia O'Keefe or if your like a music artist like Eric Clapton. You are an artist. Then there are writing artists, who their words through their stories create mental pictures in your head.