Bono is the first transgender competitor on the hit ABC show.
Cher says her son, who was born female and underwent surgery to become a man, is being "viciously attacked" on blogs and message boards since the new cast was announced Monday.
"This is Still America right? It took guts 2 do it," Cher wrote, adding that she supports him no matter what he chooses to do.
"Mothers don't stop Getting angry with stupid bigots who (mess) with their children!" the 65-year-old singer wrote.
Bono, 42, is paired with pro dancer Lacey Schwimmer on the reality show, where celebrities and their professional partners perform various ballroom dances for judges' scores and viewer votes.
"Dancing" fans have posted both angry and supportive comments on the show's message boards. One called the casting choice "disgusting" and said "ABC should be ashamed of theirselves for harassing mainstream Americans and Christains."
Another wrote: "I never and mean NEVER watch DWTS but will this season to support/vote for (Chaz)."
On his own Twitter page, Bono described himself as "the luckiest guy around" and thanked his fans for their support. He also thanked Cher. "Thanks for all your support mom," he wrote. "The haters are just motivating me to work harder and stay on DWTS as long as I possibly can."
The 13th season of "Dancing With the Stars" is set to premiere Sept. 19.
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