James Weaver, Greenback Party, 1880.
That was a truely creative answer, so I had to look it up to see what kind of results were out there.
I’m not seeing where he advocated for social justice though. If you happen to know some specifics, do share and link.
Nineteenth century social reformers tended to find one thing wrong with society (the gold standard, the tariff, monopolies, railroads, landlordism and high rents) and look for one thing to fix it (free coinage of silver, free trade, anti-trust legislation, federal regulation or ownership of railroads, the single tax). Once that was fixed they thought, things would be okay.
Earlier reformers were similar, focusing on the abolition of slavery, prohibition of liquor, the Homestead Act, women's suffrage, communal living, or changes in dress and diet. Whether anybody used the phrase "social justice" in an electoral campaign, I don't know, though Horace Greeley used the expression when he was writing for his newspaper. By the next century, you did have Roosevelt, Wilson, and Debs calling for "social justice."