The earliest (illustrated) heroic figure that associates with a symbol would appear to be The Scarlet Pimpernel. Introduced in both play & novel forms in 1905, The Scarlet Pimpernel was an English nobleman who used a Zorro-like identity to fight the French authorities. He taunted his opponents by leaving behind a playing card with the namesake flower emblazoned on it.
Later in 1919, the public was introduced to Zorro, a Mexican hero who was very similar in nature to The Scarlet Pimpernel and was known for leaving a stylized "Z" as his calling card.
Introduced in 1936, The Phantom was known for his skull motif, although it could be debated whether or not the skull was actually his emblem or logo.
This brings us to 1938, when Action Comics #1 introduced the world to Superman, a hero widely known for the "S" emblazoned across his chest. Although Superman would appear to be the first hero who actually WORE his symbol (unless you count The Phantom), he was soon followed by Batman in 1939 - a darker character with a bat symbol on his chest.