If your goal is to download actual text message data from your phone to a computer for backup or printing:
The official Android messaging app, which can also be used on tablets and computers. Download APK File
Depending on your specific goal, you may be looking for a texting app or a way to download text conversations from your phone. If your goal is to download actual text
A widely used app that provides a free U.S. phone number for unlimited texting and WiFi calling. Download APK File
This app can create a file (XML) containing your entire message history, which you can then save to cloud storage or a PC.