RSync is traditionally used to update Gentoo portage tree.
But it's somewhat slow when dealing with a large number of files.
So, I want to try to replace RSync with Git.
I know that Funtoo have Git-based portage tree, but is there a Gentoo-specific official one?
As a Gentoo developer I can say that there is no official git repository for the portage tree. There are plans to switch from what is currently used, CVS, to git, but that may still take a while.
Currently, there are three ways to get the tree:
Via rsync, as you mentioned.
Via CVS, commands for anonymous access and online browsing can be found here. Updating is done with cvs update which is probably slower than rsync.
By downloading a tarball of a portage snapshot from your nearest mirror, generated daily.
All other ways aren't official (such as the funtoo git repository mentioned in another answer), although they may be what you're looking for.