Zuma, who is running for a new opposition party, has appealed a decision by electoral officials to bar him from the vote over a 2021 conviction.
On Monday, the 81-year-old was in court in Johannesburg as lawyers debated the case.
"If the masses want me to be president, what's going to stop them?" a cheery Zuma told supporters, after the hearing. "Allow me to go and finish what I started."
South Africa is to hold general elections on May 29 in what is expected to be the most competitive vote since the advent of democracy in 1994.
The ruling African National Congress (ANC) is struggling in the polls and risks losing its parliamentary majority for the first time since the end of apartheid, amid a weak economy and allegations of corruption and mismanagement.
South Africans will vote for a new parliament, which in turn elects the president.
In March, the electoral commission said the constitution bars anyone convicted of an offence and sentenced to more than 12 months' imprisonment from running from office.
Zuma was sentenced to 15 months in jail in June 2021 after refusing to testify to a panel probing financial corruption and cronyism under his presidency.
But his lawyers have argued that the sentence does not disqualify him as it followed civil rather than criminal proceedings.
Lawyer Dali Mpofu, representing Zuma, also told the court on Monday that since his client had benefited from a remission, his sentence was really only three months long.
"We are dealing with someone who is a convict," retorted lawyer Tembeka Ngcukaitobi for the electoral commission.
Judges said they will issue a decision on Tuesday.
Zuma's ability to run could be a key factor in May.
Among the groups that seek to capitalize on the ANC's weakness is Zuma's new uMkhonto we Sizwe (MK) party.
The party largely relies on the considerable political clout still wielded by Zuma, who despite scandals and graft allegations is still popular, particularly among the country's more than 10 million Zulus.
The electoral commission is expected to publish the final candidate list on Wednesday.
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