Although the donkey is used as a symbol of the U.S. Democratic Party, it has never been officially adopted. The rooster, however, was. The story begins in 1840, when the famous "Log Cabin Campaign" occurred. More on that shortly. It must be said that the donkey did come first. In 1828, Democrat Andrew Jackson was ridiculed and called a "jackass" by the supporters of John Quincy Adams during the heated presidential campaign. In 1870, Thomas Nast used it as a symbol for the Democratic Party. And it has been widely recognized as the party's unofficial symbol since that time.
Now for the rooster. According to John Fowler Mitchell, Jr., the origin of the rooster as the emblem of the Democratic Party was in Greenfield, Indiana. Joseph Chapman, a native of Greenfield, a Jacksonian Democrat, and a state legislator, was an acclaimed orator and derided by the opposition Whigs for his "crowing." During his campaign for a seat in the lower house of the Indiana State Legislature, the Whigs' critical "Crow, Chapman, Crow!" was seized by the Democrats and used in support of their candidate and Chapman won, despite the Whigs' nationwide victory that year. Indiana Democrats, followed by the national party, soon chose the rooster as their symbol, and Chapman was hereafter known as "Crowing Joe Chapman."
A century or so later, the rooster was seen on a poster in support of Franklin D. Roosevelt and Harry S Truman, and is still evident on posters in some states.