Shiromini Satkunarajah, 20, who was born in Sri Lanka but has lived in the UK for eight years, is due to finish her electrical engineering degree this summer.
She was arrested on Tuesday and taken to a detention centre to await deportation on 28 February.
The Home Office said it did not routinely comment on individual cases. Miss Satkunarajah arrived in the UK in 2009 as a dependant on her father’s student visa.
He died in 2011 but she and her mother were allowed to stay while she completed her secondary education and started a university course.
Further grants of Leave to Remain and of asylum were denied, but Miss Satkunarajah has been allowed to stay in the UK while appealing.
On 21 February, she was told that her asylum application had been rejected and has now launched a petition calling on the home secretary to reconsider.
More than 11,500 people had signed it on Saturday night.
“I was handed the refusal letter which states ‘You do not have a right to appeal or administrative review against the decision to refuse your application’,” she said.
“I seek for help from everyone to overturn the decision to deport me on 28 February.”
A family member, who asked not to be named, told BBC Wales: “It is not fair that she only has three months left to finish her degree. At least let her finish that.
“Shiromini came here when she was 12, her friends and family are here. She knows no-one and has nothing at all in Sri Lanka.”
Iestyn Pierce, head of electrical engineering at Bangor University, described her as an “exceptionally able and diligent” student on course for a first class honours degree.
“Shiromini figures among the very best students, having secured very high grades in her examinations this January,” he added.
“If allowed to graduate she would be sure to be a valuable member of the workforce in what is a world-wide shortage subject.”