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?
From what I can see, the Gentoo repository doesn't come with a (D)VCS repo.
The only exception being this godin-gentoo-repository, which is actually only his copy of my local overlay/repository.
So that leave you with a list of Git repos hosting to chose from, and an initial import of a rsync of that tree in your very own Git repo.
The update process would still be slow (rsynch + git add -A + git commit -m) for you, but would be a lot quicker for your Git Gentoo repo followers ;)
Funtoo has not only it's own Funtoo portage tree via Git, but they also keep a plain Gentoo portage tree via Git, as well. You can configure Funtoo to use the Gentoo branch, and then you basically have an "official" Gentoo portage tree via Git.
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.
See the gentoo-scm list for up to date information on the git migration of portage: http://archives.gentoo.org/gentoo-scm/msg_57eaa893711e1b63faa4502e8921376b.xml
Short: Not yet, but they are working on switching to git.
Difference to funtoo: The tree will have the whole cvs history.