Ms Anthony was arrested in violation of laws permitting only men to vote.
Mr Trump’s move comes amid an outcry over Postal Service disruptions that Democrats say endanger the voting rights of millions of Americans who would vote by post in November’s general election during the coronavirus pandemic.
The president has denied asking for the post to be delayed even as he levelled fresh criticism on mail-in voting.
Comments from Mr Trump and some of those assembled for a White House event commemorating the 19th Amendment of the US Constitution quickly pivoted into an appeal for re-election.
“Win, lose or draw, we have to get it right,” Mr Trump said, adding that mail-in voting, as opposed to absentee voting, leads to ballots cast by pets and the deceased.
“We have to have honest voting. That’s what this is all about here. We have to have honest voting.”
Mr Trump said he would sign “a full and complete pardon” on Tuesday, the 100-year anniversary of the ratification of the 19th Amendment – also known as the Susan B Anthony Amendment – which ensured women the right to vote.
Ms Anthony is best known for her role in the movement to secure voting rights for women but she also was a strong anti-slavery and voting rights pioneer.
Mr Trump’s action comes as his support has been eroding among suburban white women in battleground states since his last campaign.
In recent weeks, Mr Trump has recognised he needs to work to undo some of the damage among the pivotal constituency and has stepped up his events aimed at women.
His campaign has launched a “women for Trump” bus tour and the president has embraced a “law and order” message with renewed vigour.
Ms Anthony was arrested for voting in her hometown of Rochester, New York, and convicted in a widely publicised trial.
Although she refused to pay the fine, the authorities declined to take further action.
Visiting Ms Anthony’s grave site in Rochester on election day has become a popular ritual in recent years and thousands turned out in 2016 for the presidential match-up between Mr Trump and Hillary Clinton.
In 2018, dozens of voters put “I Voted” stickers on her headstone.
