Can you back up text messages on icloud?

Start by clicking on the link (the text in blue) in Jeffrey A.'s post above.

However, if you use Messages in iCloud, your messages will NOT be backed up. They are backed up automatically to iCloud (assuming you're backing up to iCloud) as long as you DO NOT enable Messages in iCloud.

How to back up your iPhone, iPad, and iPod touch with iCloud - Apple Support

Here's an Excerpt from the Use Messages in iCloud support article which I believe should answer your question:

You can use Messages in iCloud on your iPhone, iPad, iPod touch, Apple Watch and Mac. For your privacy, Messages in iCloud is end-to-end encrypted, which means you can't view or access Messages online via browser.

The article goes into further details, so it is well worth a read if you'd like to better understand how the service operates.