It says Donald Trump's running mate, a long-time opponent of Planned Parenthood, will be sent a gift certificate for every donation someone makes.
The campaign began in 2011 when as an Indiana congressman he introduced several anti-abortion measures.
They included the first bill to strip the provider of all federal funding, the BBC report said.
As the Indiana governor, Pence signed an anti-abortion bill in March this year that is seen as one of the most restrictive in the US, barring abortion in Indiana on the basis of disability, gender or race of the foetus.
Parts of that law were blocked by the courts, but not until after a social media backlash which saw women phoning or tweeting Pence details about their menstrual cycles under the hash tag #periodsforpence.
There had already been a significant rise in donations to the country's biggest abortion provider in the wake of Trump's election last week, the BBC reported.
But then over the weekend, many women went on social media to say they had made a donation in Mike Pence's name, it said.