Users can tweet at Jackman's Twitter page, @RealHughJackman, naming their chosen charity and their reason for nominating it.
Jackman will give the $100,000 to the charity named in the best tweet, which will be announced on Friday April 24.
Suggestions that have been tweeted to the actor include one from @JenTheArmyWife who said "Soldiersangels.org. They 'adopt' soldiers overseas sending them needed supplies and support. No Soldier left behind!".
Another tweet by Evanslusher says: "80% of the diseases in the developing world is waterborne. Clean water changes everything."
Another by @tvshowgenerator suggests: "GLSEN - An organization to end anti-gay bullying in schools. Taunts cause emotional damage and have at times led to suicide."
Jackman responded to the tweets by posting on his Twitter page: "Your suggestions have been informative, touching and inspiring.
"Please keep them coming. You are educating thousands by sharing your causes."
Jackman's latest movie 'X-Men Origins: Wolverine' is out in UK cinemas on April 29.
Elsewhere on Twitter, Oprah Winfrey has signed up. The TV host is yet to tweet but already has over 60,000 followers.