Transfer data from broken iphone to new iphone

If you had iCloud backup enabled, you can restore the new phone from the backup.

If you did not, then you can't transfer your data.

Some third-party shops may be willing to help by putting on a good screen so you can recover your data. This will likely void any service from Apple.

~Lyssa

You need a working device to make an iCloud or iTunes backup to then restore to a new device.