Standard practice in English is to identify the person responsible for a creative work by a different name depending on the form of the creative work. Thus, the author of a painting is a painter (or artist), the author of a sculpture is a sculptor (or artist), the author of a piece of music is a composer (or songwriter), the author of a dance is a choreographer, the author of a theatrical set is a set designer, the author of a map is a cartographer, and so on.
Of course, in many subcategories of writing, we use more-specific terms than author, too—for example, novelist, essayist, screenwriter, poet, and biographer. But few English speakers would blink if you called any of these creators an author.
In the visual arts, the broad term corresponding to author in the written arts, and applicable to a painter, sculptor, engraver, drawer, embroiderer, weaver, etc., is artist. Unfortunately for clarity, artist may also refer to a musical, theatrical, or other type of performer—who may or may not be the author of the work being performed.
In copyright law, though written works were long treated separately from visual works, the creators of paintings and other works of fine art have sometimes been termed "authors." For example, Chappell & Shoard, A Handy-book of the Law of Copyright (1863) has this to say about "An Act for amending the Law relating to Copyright in Works of the Fine Arts, and for repressing the Commission of Frauds in the Production and Sale of such Works" enacted on 29 July 1862:
The preamble states that by law as now established the authors of paintings, drawings and photographs have no copyright in such their works, and the provisions of the act are intended to supply this defect. The paintings, drawings and photographs in existence on the 29th July, 1862, which are now protected by the act, are those only which the author had not sold previously to that time.
Going farther back, we have this passage from J. Salmon, A Description of the Works of Art of Ancient and Modern Rome (1798):
The three pictures over the altars are by Rubens, and the frescos by Pomarancio. The Mosaic is by Peruzzi, and the basso-relievo of the Pieta by an unknown author.
To similar effect is J. Steward, The Stranger's Guide to Paris (1837), in this excerpt from a lengthy description of "some splendid paintings" in the aisle around the choir at St.-Etienne-du-Mont:
Ste.-Geneviève is represented in glory; below are the city officers in full costume, and a number of spectators, among whom are the poet Santeuil, and the author of the painting—Largillière;
And from John Cassell (publisher), The Works of Eminent Masters in Painting, Sculpture, Architecture, and Decorative Art (1854), we have this sentence:
An Italian writer, named Gargani, believed that he had discovered the author of the painting ["The Last Supper" of St. Onofro] to be none other than Neri di Biel, on account of a manuscript, bearing the date 1461, declaring that a picture of "The Last Supper" was painted on the walls of the refectory of St. Onofro by that artist.
Just as inexplicable as the tendency of English speakers to treat author as a mistake when applied to a painter or other fine artist is their willingness to use author to refer figuratively to God (unless, perhaps, they take "In the beginning was the Word" literally) and other nonhuman agencies. For instance, in John Ovington, A Voyage to Suratt, in the Year, 1689 (1696):
Asia we know was the first Stage of Mortals, which both for Riches and Extent, is the most considerable part of our Tripartite Continent, and enjoys a temperature of Air, by its convenient position, equally superior to both. And as it was the first Original of Mankind, by a peculiar Favour from the Supreme Author of the World; so it was likewise of Nations and Kingdoms, of Monarchies and Empires, whose Laws as well Sacred as Civil, were formed here; and those Diviner Mysteries of the Jewish, as well as Christian Religion were first explain'd.
And from John Nickolson (printer), "A Short View of the Epicurean Philosophy," in The Lives of the Ancient Philosophers (1702):
As the World was generated, and is govern'd by Nature, so 'twill have an End. For all Compositions are dissoluble, and whatever has a Beginning has an End. The Incessant Motion of the Atoms, of which it consists, must at length cause its Dissolution; not to mention that some Extrinsical Cause may be the Author of its Destruction, especially, considering that though 'tis produc'd but one way, it may be destroy'd many Ways.
Under the circumstances, it is truly odd that English resists calling the creators of works of fine art authors—but unmistakably it does.