This is an odd question, because one wonders what is meant by "Celtic." It appears to me that there is clearly a lot of Celtic influence on British music, but figuring out which song is originally Celtic and which Germanic is much harder than untangling African and European influences in American music. Which is awfully unreliable and mostly an exercise in futility, or maybe ideology.

If you are asking, what are some American songs that come from Ireland, "Skip to my Loo" is often mentioned.