Sorry, but you cannot sign the form online. You can generate a completed Voter Registration/Ballot Request form with the voter registration system on this website, but you still have to download and print the completed form and sign it.
Your original signature is needed on file by the election official. Most states require that you send the original hard copy, paper application in addition to any fax or email that you might send.
Assume this is the case for your state. Sending the form by fax or email to your election official ahead of mailing it, can be a good method to speed registration, but if you don't send your original signed form by postal mail as well, then your application (in some cases) will not be accepted. Options for voter materials transmission can be found in the State Voter Information Directory on this website.
The mailing address for mailing your Voter Registration/Ballot Request form will be provided in a personalized instruction letter to you, which is printed out with your completed form.