You can leverage an existing audience to spread the word for you.
Once you've built an initial audience, they will be the best at evangelizing the great content you produce. In social media this is very intuitive and people share links. Text is more closed off and so you should remind and prompt your subscribers on the best way to share your signup with their friends.
A great tool for this is a pre-made Subtext share image. The Subtext team is happy to create a customized version of the image below which you can send in a broadcast and ask your audience to screenshot it and share with their friends via text. This is a text-native way to share the information. You might also include a link to the signup page.