The short answer is No. United States allows foreign nationals to naturalize and become U.S. citizens and the country also allows people to hold dual nationality. People who are citizens of foreign countries may become U.S. citizens and they may not be required to give up their current nationality.
Renouncing your previous citizenship is not really up to the U.S. Government but rather your previous country. Citizenship laws differ from country to country and some countries do not allow the citizens to hold dual citizenship.
https://www.uscitizenship.info/us-citizenship/give-up-previous-citizenship-after-becoming-us-citizen/