In the January 15, 1870 issue of Harper’s Weekly Thomas Nast published his first Democratic Donkey cartoon. The repeated use of the image by the Dean of American Editorial Cartooning insured that the symbol would become lasting. By the 1880s it was understood by all that The Donkey equaled The Democrats.
The above cartoon is often called the first use of the donkey as a stand-in for Democrats; as is often the case (think Yellow Kid as the first comic strip) it is not.
The donkey equals Democrats meme started with Andrew Jackson running for president. Wits of the era couldn’t resist the Jackson/jackass similarity. What they didn’t count on was Jackson embracing the idea. Soon cartoons of a jackass with Jackson’s face started appearing and continued throughout his two terms (1829-1837).
above 1830s
By the end of the Jackson presidency he would be shown riding the jackass instead of being the jackass, and the donkey was on its way to symbolize the Democratic Party.
above 1837
Through the years leading up to The Civil War the imagery persisted.
above 1844
above 1856
above 1860
So while Thomas Nast did not created the imagery, it is undeniable that he fostered its use to such a degree that the donkey and the Democratic Party became permanently linked.
Less than five years later his Republican as elephant cartoon would appear.
Though, again, the connection had been made years before Nast.
above 1874
above 1860
Further reading: