Wagner, which has troops and business interests in the country, is providing security for the referendum.
The main opposition has called for a boycott of the referendum, accusing President Faustin-Archange Touadéra of wanting to become president-for-life.
Mr Touadéra has grown ties with Russia since French forces withdrew in 2022.
His supporters say that constitutional limits on presidential terms are “uncommon” in the region. The say the proposed changes will help achieve stability and development.
The CAR has been plagued by rebellions and coups for decades. A powerful coalition of rebel groups has been trying to oust Mr Touadéra.
On Wednesday, Wagner boss Yevgeny Prigozhin said hundreds of its fighters had arrived in the resource-rich country as part of “a planned rotation before the referendum”, according to the Afrique Media website linked to the Russian group.
It quoted Mr Prigozhin as saying that, “we control the territory of CAR. We are convinced that the gangs will not be able to harass the population”.
A UN peacekeeping in CAR is also providing security for the referendum.
But Wagner is increasingly seen as the main group on which Mr Touadéra’s government relies to remain in power, and to fight rebels.
Wagner group has had at least 1,000 forces in CAR since 2018. The group has also developed huge business interests in the country.
It reportedly trades in the minerals and timber industries.
Earlier this week, Mr Prigozhin was photographed shaking hands with Ambassador Freddy Mapouka. Mr Mapouka, a CAR presidential advisor, was in attendance at the Russia-Africa summit in St Petersburg.
France, the former colonial power, pulled its last forces out of CAR in 2022. It first sent about 1,600 troops to the country after a coup in 2013 unleashed a civil war.
As CAR moved to restore democracy, Mr Touadéra was elected president in 2016 and won a second term in 2020.
But he has been accused of becoming increasingly authoritarian. His critics further say the referendum is the latest sign of his attempt to extend his power.
If the changes to the constitution are approved, it would allow Mr Touadéra to seek a third term in 2025.
It would also raise the presidential term from five to seven years and allow the president to appoint more judges to the Supreme Court.
