Even though your Tablet PC may not be supporting SIM-cards and thus can't receive SMS, you still can sign up for a Tango account, easily.
Sign up using Google! If you are using an Android tablet, chances are, you already have a Google account. Use Sign up with Google to get an account without a phone number.
Enter you phone number and use your mobile phone to receive the SMS - do it once to sign in, and that's it.