In The Letters of J.R.R. Tolkien by Humphrey Carpenter (assisted by Christopher Tolkien), footnote 94 states:
What is meant is that it was Arwen who first thought of sending Frodo into the West, and put in a plea for him to Gandalf (direct or through Galadriel, or both), and she used her own renunciation of the right to go West as an argument. Her renunciation and suffering were related to and enmeshed with Frodo's : both were parts of a plan for the regeneration of the state of Men. Her prayer might therefore be specially effective, and her plan have a certain equity of exchange.
I don't remember that being mentioned in The Lord of the Rings, not even in the appendices. Where (in published or posthumous material) did J.R.R. Tolkien make Arwen's role explicit?