Nope. The oldest socialistic party in the US was the Socialist Labor Party, which was just a low-level thing in the 1880's and 1890's. Its only real political venture was the NYC mayoral election, which it lost.
The SLP joined with the Social-Democratic Party, founded in 1898, to become the Socialist Party of America in 1901. Their first successful venture was Victor L. Berger's congressional run in 1911, and Meyer London in 1915. They would serve on-and-off in Congress, the only members of that body from the Socialist Party. Over seventy mayors and numerous state legislators were from the SPA; Eugene Debs ran for president five times between 1900 and 1920, but lost every time, obviously.
But their political activity was mostly in the early 20th century. There were no socialist parties in the US during the 1870's, or even in most of Europe. Hell, the oldest socialist party in the world, the Social Democratic Party of Germany, was only founded in 1875.