On January 15, 1870, the donkey was first used as symbol of Democratic Party in Harper's Weekly. From the article:
"Election 101: How did the Republican and Democratic parties get their animal symbols?
Why the elephant and the donkey?
The Democratic Party’s donkey and the Republican Party’s elephant have been on the political scene since the 19th century. The origins of the Democratic donkey can be traced to the 1828 presidential campaign of Andrew Jackson. During that race, opponents of Jackson called him a jackass. However, rather than rejecting the label, Jackson, a hero of the War of 1812 who later served in the U.S. House of Representatives and U.S. Senate, was amused by it and included an image of the animal in his campaign posters. Jackson went on to defeat incumbent John Quincy Adams and serve as America’s first Democratic president. In the 1870s, influential political cartoonist Thomas Nast helped popularize the donkey as a symbol for the entire Democratic Party.
The Republican Party was formed in 1854 and six years later Abraham Lincoln became its first member elected to the White House. An image of an elephant was featured as a Republican symbol in at least one political cartoon and a newspaper illustration during the Civil War (when “seeing the elephant” was an expression used by soldiers to mean experiencing combat), but the pachyderm didn’t start to take hold as a GOP symbol until Thomas Nast, who’s considered the father of the modern political cartoon, used it in an 1874 Harper’s Weekly cartoon. Titled “The Third-Term Panic,” Nast’s drawing mocked the New York Herald, which had been critical of President Ulysses Grant’s rumored bid for a third term, and portrayed various interest groups as animals, including an elephant labeled “the Republican vote,” which was shown standing at the edge of a pit. Nast employed the elephant to represent Republicans in additional cartoons during the 1870s, and by 1880 other cartoonists were using the creature to symbolize the party.
Along with the donkey and elephant, the German-born Nast is associated with another political animal, the ferocious Tammany Tiger, which the crusading artist famously featured in an 1871 Harper’s Weekly cartoon that attacked New York’s William “Boss” Tweed and Tammany Hall, his corrupt political machine. Not all of Nast’s work was about politics, though; he’s also credited with creating the modern image of Santa Claus."