Whatsapp uses internet for messaging, but it requires a phone number to register it. Once you register it, all you need is internet connectivity. Tablet users with only wifi can still register and activate whatsapp on their device in few simple steps, as long as they have a phone and a number and this phone doesn't even need to be a smart phone.
Method A) Register new account using an available phone number
Step 1) Temporarily change the security setting to allow the Android to install apps from unknown sources.
Go to Settings → Security → Unknown sources and check the box for "Allow installation of applications from both trusted and unknown sources". This will let you install an app outside playstore.
Step 2) Download Whatsapp.apk from this link here
Step 3) Install Whatsapp apk file.
Step 4) Whatsapp will ask your phone number for verification. Enter your number complete with country code.
Step 5)You will shortly receive the verification SMS with the activation code. The message goes like this:
Whatsapp code ***-***. You can also tap on this link to verify your phone: v.whatsapp.com/******
Since you can't do SMS verification on your Wifi only tablet, open the browser on the tablet and type the link from the SMS v.whatsapp.com/******
(****** denotes the 6 digit activation code)
Step 6)Whatsapp is now registered on your tablet with the phone number you provided.
The only problem with this is, if the phone number is already registered for whatsapp from some other smartphone, it will stop working on that phone when you register it using the tablet.
Method B) Get a mirror of existing account using the new Whatsapp Web
If all you need is access to the same whatsapp account from both your smartphone and your wifi tablet or any other device, you can make use of the newly launched official Whatsapp Web client. This one is simply an extension to your phone and lets you open a mirror of your whatsapp conversations on a chrome browser on another supported device. This currently works on Android, Windows Phone, and BlackBerry but not on iphones due to iOS limitations.
Step 1) Open the following link in chrome:
(If you dont have chrome on your tablet, get it from play store)
Step 2) Scan the QR code using your smartphone which already has whatsapp on it. If you have latest version of whatsapp the web version option is built-in and so is the scanner.
Your phone is now paired to the Whatsapp web client and you can see a mirror of all your chats and conversations.
This works as long as your phone is connected to the internet.