how do i connect my iphone to itunes if sscreen is broken

You get the iPhone display repaired.

Backups have to happen before the loss/damage/dunking.

Whether the data can be preserved depends on the damage and the available repairs.

Ise the Get Support link in the upper right of this webpage, and discuss your options and alternatives with Apple.

Did you try having the screen repaired? That’s the only way that I know of to achieve what you're trying to do.

Fix the screen first