Well, kind of.
If you are signing up for a new account on Tango, you cannot use Google Voice number, because will not be receiving a confirmation code. We can't send those to Google Voice, sorry!
However, if you already have a Tango account, you can add Google Voice number to your profile and use it to log in - you will be receiving authorization codes through another device that is already connected to Tango.
If you are using Google Voice number and you are unable to log in, please contact customer support for assistance.