Since the access code is sent to the telephone number which you're registering, you must have an active phone number in order to receive the access code. This can also be a temporary number, used only for the setup of Viber. e.g. phone card, landline etc.
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I do not think that you can use Viber without a phone number. The application does not create an account and thus uses your phone number as your identity to allow you make free Viber call to your friends using their phone numbers.