Backup iphone with broken screen

You can't manually. If you're lucky you had it set to backup to iCloud automatically. In that case -- and if the phone can still function to some degree -- connect it to the charger in a location where it can use WiFi and hope it will back up.

In: How to back up your iPhone, iPad, and iPod touch

https://support.apple.com/HT203977

see the section: "Automatically back up with iCloud Backup

To let iCloud automatically back up your device each day, here's what you need to do:

Make sure that iCloud Backup is turned on in Settings > [your name] > iCloud > iCloud Backup.

Connect your device to a power source.

Connect your device to a Wi-Fi network.

Make sure that your device's screen is locked.

Check that you have enough available space in iCloud for the backup."

Note some things are not stored in a backup which means if you have set these to sync automatically then they are always backed up in iCloud. Click on this link and read "About missing information after you restore your iOS device with iCloud Backup" -->

https://support.apple.com/HT203768