There isn't an epigraph exactly, but there is a totally on-point "Preface." (Read the Preface here.)
The Preface is a little confusing at first glance—we open a novel expecting to find something along the lines of "Once upon a time…" and instead, we're met with the sweeping claim that "The artist is the creator of beautiful things." This seems totally, totally random, but it actually is very appropriate, both to this novel in particular, and to Wilde's body of work in general.
Critics at the time weren't always the biggest fans of Wilde's work—especially Dorian Gray, which was derided for its so-called "sham moral" at the time—so it's understandable that he had a bone or two to pick with his detractors.
One of the common complaints about Wilde's novel was that it didn't take a strong moral stance, and that it demonstrated the author's own immorality (Wilde was a famously scandalous celebrity). Frustrated with these goody-two-shoes critics, Wilde responded that they had committed "the unpardonable crime of trying to confuse the artist with his subject matter."
This page-long preface, which appeared in the new and revised 1891 version of Dorian Gray (the first was published in 1890), succinctly sums up Wilde's point of view about art: in a nutshell, the artist is not concerned with morals and ethics when creating his art, but simply attempts to make something beautiful. Readers see what they want to see in the novel, so they only have themselves to blame if they find it scandalous.