It was established in 1860 by railroad workers some of whom came to the US from their mediterranean island home. It was they who decided it would be a good idea to name their new settlement in honour of their home, Corsica.
Prompted by this I have delved a little further and discovered that Blooming Grove in Morrow County, Ohio was originally named Corsica! The town was established in 1822 by Salmon E. Harding who apparently was greatly inspired by Napoleon. The town was renamed Blooming Grove in 1835.
There's more - in Pennsylvania there is a Borough called Corsica in Jefferson County, population 354, established 1802 by John Scott. The name also appears to have been inspired by the French Emperor of the time, Napoleon.
Napoleon clearly had an inspirational impact in the US as did Pascal Paoli another of Corsica's favourite sons as there are numerous places named in honour of them both.