I don't have any Google Services installed.
So I tried finding it on F-Droid, but it wasn't there. I found out there has been a lot of discussion about this. [0][1]
I decided to compile it on my own. That requires to use use Google Libraries, oh well. I managed to get that done and was disappointed when I tried to use it. It also requires to have Google Services installed on your phone for push notifications. I don't have that.
I tried finding a solution, and other people complained about this and there was the idea to use websockets instead of google push notifications [3]. Someone forked TextSecure and started working on it [4].
Unfortunately that fork isn't stable yet, and it doesn't communicate with 'producion' users of TextSecure [5].
This is where I gave up. It shouldn't be so hard to install a free app on a free system.
Also, the websocket fork is somewhat dead [6].
0: https://f-droid.org/posts/security-notice-textsecure/
1: https://github.com/WhisperSystems/TextSecure/issues/127
3: https://github.com/WhisperSystems/TextSecure/issues/1000
4: https://github.com/JavaJens/TextSecure