What size of ground wire do I need to run between two ground rods?
Without getting into too many details and situations, generally, for a 200 Amp service, if you are only concerned about the wire between two ground rods, #6 Bare Stranded Copper wire will do just fine.

There are some parameters to keep in mind.  #6 Bare Stranded Copper wire must be protected.  Usually, the wire should be under 1 foot of dirt cover, or protected by some form of construction.

A #4 Bare Stranded Copper does not need the same protection and the extra money involved may be worth it if you are installing it in very rocky soil.

Keep in mind that this is a very general answer and the details of a particular job may require a different answer.