Iphone 6 screen is broken so I can't put in passcode to backup phone. Is there anything I can do?

Old thread, but here's the answer. Most likely no. You could plug a wired lightning keyboard in and enter your passcode, but if the touchscreen isn't functional, you won't be able to hit the "Trust" button when you try to backup via iTunes. If you've ever sync'ed with iTunes on that computer before, however, then you may not be asked to Trust your computer. In that case, buy a wired keyboard and unlock your iPhone before plugging into iTunes.

Another option would be to take it to a screen repair shop and ask them if they can temporarily connect a replacement touch screen so you can get in and backup your phone.

. If you've ever sync'ed with iTunes on that computer before, however, then you may not be asked to Trust your computer.

If the phone was previously backed up to iTunes, you will not be asked to trust or enter password at all. Password is required only when Restoring from the backup.