Immigrants who become naturalized US citizens DO take a citizenship test.

"Perhaps one of the most intimidating components of the naturalization process is the citizenship test, which gauges applicants' knowledge and understanding of United States history, government, and the legal system. The test often contains information that many native born U.S. citizens don't even know, believe it or not. Proper preparation is essential to passing this important part of the citizenship application process. This section provides resources to help applicants prepare for the citizenship test, including a list of typical citizenship examination questions and an overview of what to expect on the test."

https://www.findlaw.com/immigration/citizenship/citizenship-test.html

Examples of test questions: https://www.findlaw.com/immigration/citizenship/typical-citizenship-examination-questions.html