Yes. It is legal to buy cryptocurrencies in the USA and they are taxed like property by the IRS.
From the WIKI:
The U.S. Treasury classified bitcoin as a convertible decentralized
virtual currency in 2013. The Commodity Futures Trading
Commission, CFTC, classified bitcoin as a commodity in September 2015.
Per IRS, bitcoin is taxed as a property.
In September 2016, a federal judge ruled that "Bitcoins are funds
within the plain meaning of that term".
 "Statement of Jennifer Shasky Calvery, Director Financial Crimes
Enforcement Network United States Department of the Treasury Before
the United States Senate Committee on Banking, Housing, and Urban
Affairs Subcommittee on National Security and International Trade and
Finance Subcommittee on Economic Policy". fincen.gov. Financial Crimes
Enforcement Network. 19 November 2013. Retrieved 1 June 2014.
 "IRS Virtual Currency Guidance : Virtual Currency Is Treated as
Property for U.S. Federal Tax Purposes; General Rules for Property
Transactions Apply". www.irs.gov. Retrieved 2017-04-22.