No, online voting is not currently allowed in the United States. Some uniformed and overseas citizens can vote by fax or e-mail if their state accepts absentee ballots in these formats.
Uniformed Service Members and Other Overseas Citizens
The Uniformed and Overseas Citizens Absentee Voting Act (UOCAVA) of 1986 allows you to vote absentee in local, state and federal elections if you are a U.S. citizen, 18 years or older, and an active duty member of the Armed Forces, Merchant Marine, Public Health Service, NOAA, a family member of the above, or a U.S. citizen residing outside the United States.
Many states allow absentee voters that meet UOCAVA requirements to submit their ballot by fax or as a scan attached to an e-mail.
Residents Displaced by Hurricane Sandy
The state of New Jersey recently extended coverage of UOCAVA (PDF) to residents to who have been displaced by Hurricane Sandy. People who meet the requirements may be able to vote by fax or e-mail.
Challenges With Online Voting
The 2002 Help America Vote Act established the U.S. Election Assistance Commission (EAC) to help administer federal elections, including certifying voting systems. The Act also directs the National Institute of Standards and Technology (NIST) to research and make recommendations to the EAC regarding voting security and privacy.
NIST has done research on remote voting technologies and they have concluded that current Internet Voting Systems are not as secure as in person voting. Problems such as malware on personal computers and the lack of electronic voter authentication would reduce confidence in the results.
Read NIST’s report on Security Considerations for Remote Electronic UOCAVA Voting (PDF).