Yes. Major international exchanges will all likely comply with Foreign Account Tax Compliance Act (FATCA) or simply refuse U.S. clients.
Well, there's Bitfinex who also let's you use USD to buy Monero, not sure if they require SSN for wire deposits. As an alternative, if you don't want to give your blood or make a human sacrifice, you can use localmonero.co
Monero project lead Riccardo Spagni and Litecoin founder Charlie Lee discuss benefits of XMR+LTC partnership: