And nearly six in 10 think he acted inappropriately in storing boxes of classified information at his Florida residence, compared to 26 per cent who believe he was in the right, according to the Quinnipiac University survey.
More than three-quarters (76 per cent) of Americans said they were following news of the raid on Mar-a-Lago closely.
And just under two-thirds (64 per cent) of voters polled said they thought the allegations were either very serious or serious.
“While the Justice Department weighs the evidence, Americans have been watching closely and have their own verdict: former President Trump’s alleged hoarding of classified documents was very serious, very wrong, and half of Americans believe it was a criminal act,” Quinnipiac University Polling Analyst Tim Malloy said.
The figures were split along political allegiances.
Eighty six per cent of Democrats said Mr Trump should be prosecuted, compared to just nine per cent of Republicans.
Meanwhile, 67 per cent of those polled said they believed US democracy is in danger of collapse, a nine per cent increase from January.
The poll also shows encouraging signs for President Joe Biden. His job approval rating has improved from 33 per cent in July to 41 per cent, his highest figure since last September.
Fifty two per cent disapprove of his performance.
The biggest change in his approval figures came on the economy, where his approval rating improved from 28 per cent in July to 53 per cent after a string of legislative victories.
Mr Malloy called the Biden turnaround a “summer time surge”.
“President Biden’s approval number bounces back to the long elusive 40 percent mark, as he rides increased support among young adults who may well be encouraged by Biden’s decision to erase some student debt,” Mr Malloy said.
A clear majority of Americans also stated they would prefer not to see either Mr Biden or Mr Trump run again in the next presidential election.
Some 67 per cent said Mr Biden should not seek re-election, while 62 per cent don’t want Mr Trump to run for a third time in 2024.
On Thursday, a federal judge in Florida heard arguments from prosecutors and Mr Trump’s attorneys on whether to grant the former president’s request to appoint a special master to review the documents the FBI seized from his home in August.
US District Judge Aileen Cannon also said she would defer ruling now on whether to unseal a more detailed inventory of the seized property that the Justice Department has filed under seal with the court.
The documents were among the US Government’s most closely held secrets, and included sensitive intelligence gleaned from informants and signals intelligence.
Mr Trump has sought to downplay the government’s concerns, and has accused the Justice Department of escalating the situation even after he handed over boxes of documents to the National Archives and allowed FBI agents in June to visit his home.