Is there any git repository with official daily updated Gentoo portage?

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:

1. Via rsync, as you mentioned.

2. 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.

3. 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.

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 of 9th Aug, 2015, Gentoo has migrated their portage history to Git. You can check it at:

https://gitweb.gentoo.org/repo/gentoo.git

Or clone it at:

https://anongit.gentoo.org/git/repo/gentoo.git

However, there are a few things to point out:

1. The repository does not include any commits before the migration. A "git replace --graft" is proposed [1].
2. The Git portage tree does not contain metadata cache. You might need to generate by yourself using egencache or "emerge --regen".
3. The Git portage tree does not contain any news or GLSA information. They are stored at:
   • https://anongit.gentoo.org/git/data/dtd.git
   • https://anongit.gentoo.org/git/data/gentoo-news.git
   • https://anongit.gentoo.org/git/data/glsa.git

[1] https://wiki.gentoo.org/wiki/Project:Infrastructure/Git_migration