The British actor is listed on auction site www.charitybuzz.com with the current offer standing at $30,000.
The winning bidder will also get the opportunity to spend a day on the Vancouver set of `The Twilight Saga: Breaking Dawn`, the fourth movie in the `Twilight` franchise, and meet the rest of the cast including Robert`s girlfriend Kristen Stewart, Taylor Lautner and Dakota Fanning.
The auction package includes two nights at the Four Seasons Hotel in Vancouver and VIP limousine service to and from the `Breaking Dawn` set with all proceeds going to the GO Campaign which is dedicated to helping children all over the world.
Robert is not the only celebrity currently listed on the auction site.
Fans can meet the newly-engaged Prince William - who will marry his fiancee Kate Middleton in April next year - for upwards $8,000, while an audience with `Baby` hitmaker Justin Bieber currently appears less popular at $3,000.
A walk-on role in TV vampire drama `True Blood` has currently reached $10,500 in the auction.