Hello,
No, the older G4 Macs and 2010 Mac Pros have totally different slots/architecture for their graphics cards. They aren't compatible and cannot be swapped.
I have been using an Apple DVI-to-ADC Adapter for years with my trusty old 22" Apple Cinema Display (ADC). It is currently attached to a Mac mini (Mid 2007). Used adapters are still bringing prices close to or more than the original price of $99 USD.
The adapter would probably be your best bet, and should work with your Mac Pro.
C