The viral strategy needs to be a natural extension to the app that requires SMS - not sure you want to just use it for the sake of it being viral (seems forced).
A perfect example of this is the Twist app. The app tells someone you are meeting with when you will arrive. When you set up a twist a text message is sent to the person you are meeting with (if they don't have the app installed). The message says you are on your way and if they'd like to know when you will be there, download the app. It has been effective because it solves a problem, gives the end user an option and extends the usefulness of the app's original purpose.
Hope this helps!
In order to promote growth via SMS, you first have to require the user you already have acquired to provide your app permission to access their contacts.
In order to get users to opt-in to this permission, you have to provide them real perceived value upfront.
Therefore, I'd suggest starting with in-app A/B testing of the messaging around access to permissions prior to asking for contacts and looking at what drives the most number of opt-ins.
But just sending SMS isn't enough. You need for the recipient to want to open AND act on the link you're sending. In order to do this, you have to think about the value you're going to create for the recipient of that message as it ties back to the sender. Depending on what your app does, there might be lots of possibilities or only a small number of incentives that are big enough to inspire action.
Our app in private beta utilizes SMS in a pretty effective way to drive growth. Happy to share what we're doing and maybe share some ideas with you.