A group of scientists drafted the letter with the initial aim of building a network of 500 women.
In the six days since its publication, 8,800 researchers have signed the pledge, which rejects the "hateful rhetoric that was given a voice".
Dr Kelly Ramirez, at the Netherlands Insitute of Ecology, was an author.
Dr Ramirez and co-authors Jane Zelikova, Theresa Jedd, Teresa Bilinski and Jessica Metcalf took aim at discrimination targeting "minority groups, women, LGBTQIA, immigrants, and people with disabilities".
Their letter states: "Many of us feel personally threatened by this divisive and destructive rhetoric and have turned to each other for understanding, strength and a path forward".
Dr Ramirez explained on the Scientific American website that she and a group of colleagues hoped to start a positive conversation in response to "fear that the scientific progress and momentum in tackling our biggest challenges, including staving off the worst impacts of climate change, [would] come to an abrupt stop" in the wake of Donald Trump's election victory.
Mr Trump promised, during his campaign, to cancel the Paris Climate Agreement.
Dr Ramirez added: "We asked ourselves, how can we take action?"
Dr Franciska De Vries, from the University of Manchester, is also involved in this project, which has quietly gathered momentum via social media.
She said she hoped it would develop into a "global network" of scientists who would support each other in research and to inspire young women to embark on careers in science.
"It's empowering for people to read that letter and to see the huge amount of signatures and support," Dr De Vries told BBC News.
"To share these feelings with a network - we have a voice."
The researchers now plan to convert this outpouring of support into practical measures that promote scientific research and career progression, including mentoring programmes for women scientists.
"We see this as the start of something bigger," said Dr De Vries.
The American Association for the Advancement of Science has also responded to the initiative, telling the BBC: "We commend efforts to stand up and speak out on behalf of women in science and engineering."
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Almost 10,000 women working in science have signed an open letter pledging to combat discrimination and "anti-science sentiment" following the US election.