Sarah Pond said a member of staff at the Staffordshire theme park said: "You need to get off, you have one hand."
"Never in my life have I been spoken to like this," said Miss Pond. "I was not offered a reason why when I explained I have been on this ride about 10 times."
Alton Towers said it had apologised to Miss Pond, who was not allowed to ride the rollercoaster for safety reasons.
More on this story and updates from Stoke & Staffordshire
"We are in contact with her directly and will endeavour to reach a resolution," the theme park said in a statement.
Miss Pond was barred from the Smiler rollercoaster, the ride on which several people were seriously injured last year.
In a Facebook post, Miss Pond, 33, from Shrewsbury, said she had been "astonished" to see a girl with her arm in a plaster cast allowed on to the ride.
She wrote: "I read the rules of the ride. You need to be able to walk 25m without help. And climb a ladder. Well I can assure you I can, nothing is wrong with my legs!"
She added: "I'm still angry and upset. Never in my 33 years of life have I been treated with such discrimination over being born without my hand.
"I am not registered disabled as I'm too able bodied and for that reason can't claim any benefits."
A spokeswoman for the theme park said: "On arrival at the ride entrance, our staff did advise that for safety reasons, she would not be eligible to ride the Smiler.
"We aim to ensure that disabled guests are treated with respect and in a manner that is appropriate to their needs, whilst maintaining equality for all of our visitors."
Miss Pond said the experience had put her off ever going to Alton Towers again and disputed the claim she was told at the ride's entrance she could not go on the rollercoaster.
Alton Towers' owners, Merlin Attractions, face a large fine as a result of the Smiler crash last June.
Last month Merlin admitted a health and safety breach over the crash, which resulted in two women having leg amputations.
A one-handed woman who was barred from a rollercoaster at Alton Towers has accused the venue of discrimination.