Yes, and in fact in almost all states you will need a motorcycle license and not just a moped license, as a Moped is generally considered to be a cycle with a 50cc engine or smaller.
It also needs to be registered with the DMV and pass an inspection (some states do not require inspections, however - you'll need to check for yourself) AND you need to carry liability insurance to be able to LEGALLY ride it on the roads.
If you go to http://www.moped2.org/mstates.htm all the state moped drivers license requirements are listed.
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