Last month the electoral commission barred him over a contempt of court conviction.
It argued the constitution barred people from holding public office if convicted of a crime and sentenced to more than 12 months in prison.
Mr Zuma, 81, has been campaigning for the new uMkhonto we Sizwe (MK) party.
A former stalwart of the governing African National Congress (ANC), he is controversial figure and served as president from 2009 until 2018, when he had to step down because of corruption allegations.
He was sentenced to 15 months in jail in 2021 for failing to testify in a corruption investigation, though he only served three months on health grounds.
Mr Zuma’s new party is named after the ANC’s former military wing, and he sees himself as the true heir to the revolutionary roots of the party once led by Nelson Mandela.
He has been fronting the MK party’s campaign and was the first name on their candidate list.
Rather than voting directly for a president, South Africans elect members of the National Assembly. The head of whichever party can muster a majority is likely to become the country’s leader, though it could put forward another candidate.
For the first time since the start of the democratic era in 1994, the ANC’s vote share could fall below 50%, according to several opinion polls.
The MK party is seen as popular in Mr Zuma’s home region of KwaZulu-Natal.