Those who sign the petition – which pledges to support free speech and gun rights – will have to give their contact details, potentially allowing AmericaPAC to contact them about their vote.
Musk had previously offered to give $47 to anyone who got a registered swing-state voter to sign the petition.
According to Slate,, external this was legal under US election law because no-one was being paid to vote – despite introducing money into a process that could identify likely Trump voters.
Musk, who has emerged as a key Trump supporter in recent years, launched AmericaPAC in July with the aim of supporting the former president’s campaign.
He has so far donated $75m (£57.5m) to the group, which has quickly become a central player in Trump’s election campaign.
The Trump campaign is highly reliant on outside groups such as AmericaPAC to canvas voters.
A statement on the groups website reads: “America PAC was created to support these key values: Secure Borders, Safe Cities, Sensible spending, Fair Justice System, Free Speech, Right to Self-Protection.”
Musk said he wants to get “over a million, maybe two million, voters in the battleground states to sign the petition in support of the First and Second Amendment.”
“I think [it] sends a crucial message to our elected politicians,” he added.
Musk is currently the world’s richest man, with an estimated net worth of $248bn (£191bn), according to US business magazine Forbes.
The 2024 presidential race will likely come down to seven key battleground states including Pennsylvania as well as Wisconsin, North Carolina, Georgia, Michigan, Arizona and Nevada.