The ANC's new leader will be its presidential candidate in the 2019 elections, which will bring an end to Zuma's second term.
Zuma was found not guilty of raping Fezekile Kuzwayo in 2006, before he became president in 2009.
The deputy president said he appreciated how hard it was for women to lay charges of sexual assault, and when pressed further by his interviewer, added: "Yes, I would believe her".
"It must be the most hard decision a woman has to make.so yes, I would believe her".
The Presidency has released a statement in which it notes Ramaphosa's comments.
The rape allegation has haunted Zuma for years despite his acquittal in court and has remained a popular topic in South Africa as the.MeToo movement spreads.
Liberian court says presidential run-off can go ahead
The Supreme Court also ordered that NEC prohibits from voting, anyone whose name is not found on the voter roll. The apex court noted that the FRR is the only electoral document that speaks to the eligibility of voters.
During the trial, Zuma told the court he had showered after having consensual sex with his young HIV-positive accuser to avoid contracting the virus.
Having evaluated the totality of the evidence, the court acquitted Zuma of the rape charges.
He was head of the country's national AIDS council at the time, and the case fuelled public outrage over AIDS prevention and sexual violence in South Africa.
In 2005 Kuzwayo‚ also known as Khwezi‚ accused Zuma of raping her at his home in Forest Town‚ Johannesburg.
While the branch nomination numbers are the best available indicator of who's likely to win, they aren't conclusive because some bigger branches can have more than one delegate and there's no guarantee delegates will vote as instructed.