Vithiya Alphons, 24, has acute myeloid leukaemia but her Sri Lankan background makes the search hard as not many South Asian people are on donor registers.
She launched a social media campaign  to help find a match.
Charity Anthony Nolan said 5,600 have signed up in the last week.
"The impact of Vithiya's appeal has been nothing short of incredible," said Ann O'Leary, head of register development, at the charity.
"But Vithiya still needs to find her stem cell match and there are people just like her all across the world who are still waiting.
"We need to continue to diversify the register so we can find a match for all."
Miss Alphons was diagnosed with the aggressive form of blood cancer after falling ill just days after returning for her final year as an optometry student at Cardiff University.
She started feeling unwell with severe sickness and a fever, while she had a pain in her leg, so she went to her doctor for tests.
She underwent chemotherapy in Cardiff before being well enough to be transferred to a hospital in London, where she is from.
After her third course of chemotherapy, Miss Alphons felt better and thought she had beaten her illness.
But further tests showed the leukaemia was still in her blood and doctors told her the best option was a stem cell transplant from a donor, which is needed in the next two months.
Speaking to BBC's Asian Network Miss Alphons said she is grateful for all the support.
"I would just like to say thank you so much to everyone who has registered so far and please, please do carry on registering because you can save my life and you can also save so many other's lives.
"Please spread the word and help me to save my life."

Media playback is unsupported on your device
21 October 2014 Last updated at 09:51 BST
Eleven-month-old Harmonie-Rose Allen became ill in September and was rushed into Bristol Children's Hospital where she was diagnosed with a rare form of meningococcal septicaemia.
Harmonie-Rose's family want to raise money to help with her care and have stuck pink ribbons all around the estate where she lives.
BBC reporter Ali Vowles went to meet the family.

The Colin Bloomfield Melanoma Appeal was launched in February to raise awareness of skin cancer and educate children in schools about sun safety.
The target was reached on Monday after the Freemasons in Derby donated £10,000 with a new target set at £75,000.
Radio Derby presenter Colin Bloomfield - who has stage four melanoma - said the donations were "hugely generous".
BBC Radio Derby is working with the Derby Telegraph and charity Skcin, which specialises in skin cancer prevention.
The station launched the appeal after Colin's diagnosis in 2013, and his openness and optimism on the disease touched thousands of listeners.
The 33-year-old had a malignant melanoma removed from his leg 10 years ago but in 2013 he was told the cancer had returned and in November he was given months to live when it spread to his brain.
"Every single pound has made such a big difference," he said,
"As a child I never understood the seriousness of getting burnt but I'm living through it now.
"[Melanoma] is a truly horrible disease that a lot of people don't understand the seriousness of.
"We are not used to seeing the sun in this country and when we go out and enjoy it, it is about doing it safely and responsibly.
"If we can hammer home that message to kids in schools that can only be a good thing."
Earlier this month Derby County Football Club raised more than £14,000 after donating £10 for every away ticket sold at Norwich.
The appeal aims to take the sun safe scheme to 200 schools in Derbyshire and East Staffordshire.
Thousands of people have come forward following a worldwide appeal to find a stem cell donor for a Cardiff University student who needs a match in the next two months.
[NEXT_CONCEPT]
A fundraising campaign is under way to help a baby girl from Bath who has to have all of her limbs amputated after contracting meningitis.
[NEXT_CONCEPT]
A skin cancer appeal backed by a BBC presenter has reached its £45,000 target after just six weeks.