There's an app, Silence[1], which encrypts your SMS if your contact uses it as well. It does so over the actual telecom SMS network, and doesn't break non-Silence user messaging either. Been using it for years.
[1]: https://silence.im/
edit:
F-droid: https://f-droid.org/packages/org.smssecure.smssecure
Play: https://play.google.com/store/apps/details?id=org.smssecure....