how can I back up my iphone with a broken screen?

EDIT:

I'm just correcting my self:

You can NOT make a backup whether you are using PC or Mac as it always requires you to enter the code on your iPhone. You must have the screen fixed first.

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You can try to connect your iPhone to a PC or Mac - it requires that your iPhone has been connected before, otherwise you will be asked to enter your passcode. So if the screen is so damaged that you can not enter your passcode, then it can not be done.

To make a backup:

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