My iPhone screen is completly broken, can I still bakup?

I really need to bakcup my phone, but the screen is completly broken. ITunes is telling me to "allow acess through iPhone" what do I do?

It's too late for that. There's no way around it. If you didn't already have a sync relationship established between the phone that's now broken and iTunes on your computer, you are not going to be able to back it up.

The reason you're getting the message is because it is an unknown device, this is to stop people from stealing phones and creating an unencrypted backup so they can view all the files of the device. It's always best to sync at least once when you get the phone so that the phone and computer recognise each other in case something like this happens.