In a February executive order, President Donald Trump said Afrikaners - descendants of mainly Dutch settlers who arrived in the 17th Century - could be admitted as refugees as they were "victims of unjust racial discrimination".
Relations between the US and South Africa have become increasingly strained since Trump became president in January.
Saccusa said that in a "pivotal step", it has handed the list of interested individuals to the US embassy in Pretoria.
An embassy official confirmed to the BBC that it had received the list.
Out of the 67,042 people who registered on Saccusa's site, most had Afrikaner or English names, the organisation's president, Neil Diamond, said.