One of the common elements that most of our ancestors had in their background was an American Naturalization Ceremony. Only if some of your folks arrived prior to 1820 might they have avoided one of those.
If you want to see what it's all about, visit the International Festival at the State Fairgrounds this Friday around 3 pm. The Sons of the American Revolution will be there in uniform and they are a popular photo op for the new citizens. You can also visit the booths of your ancestral homelands.
Around 200 new Americans will be sworn in that day, and it is always an impressive sight to see so many individuals from around the world who have taken the time, expense, and effort to become U.S. citizens. Check it out--it will restore your faith in our country.