Trump, who has said that he may stand for election against President Obama, publicly criticised the Democratic party leader and questioned the legitimacy of his term of office in recent weeks.
President Obama's administration then took the decision to end speculation by releasing his unedited birth certificate.
According to the Huffington Post, former White House staffer and Twitter employee Katie Jacobs approached the Apprentice star at the White House Correspondents Dinner last weekend.
She then tweeted: "Dear America, you are welcome #theDonald... And the autograph," before adding links to images of her meeting Trump and the signed document.
Jacobs has since put the item up for auction via eBay Giving Works, with 100% of the funds raised going to international education charity Room to Read.
Trump has been criticised by a number of high-profile celebrities, including outspoken Obama supporter Cher, who blasted the entrepreneur for previous comments.
The US President subsequently slammed Trump at the White House event, drawing criticism from the TV personality for publicly mocking him.
However, Trump later congratulated the president on his efforts to bring terrorist Osama Bin Laden to justice.