Yes, U.S. citizens can use Binance. However, they cannot use the main exchange site, Binance.com. Instead, they must use a different site, Binance.us.
NOTE: WARNING: US Citizens should be aware that using Binance may be in violation of U.S. laws and regulations. US citizens are subject to stringent regulations when trading cryptocurrencies, and Binance may not comply with all of those regulations. Furthermore, it is possible that using Binance could result in civil or criminal penalties under US law. It is important to consult a licensed financial advisor or lawyer prior to using Binance if you are a US citizen.
Binance.us is a separate entity from Binance.com, and it is subject to different regulations. As such, it has different rules regarding who can use it. Currently, only residents of California, New York, Montana, and Florida are able to use Binance.