Does Bit torrent work with Gentoo?
 

I know it works with Red hat, and debian.

if it does work , how?

A distribution is just a collection of software. With the expection of some configuration tools which might be distribution specific pretty much any other peice of software is availible for seperate download and can be installed on any Linux distribution.

Looking in protage (Gentoo Package System), three things come up when searching for bittorrent:

* net-p2p/bittorrent
Latest version available: 3.3.0
Latest version installed: [ Not Installed ]
Size of downloaded files: 164 kB
Homepage: http://bitconjurer.org/BitTorrent
Description: BitTorrent is a tool for distributing files via a distributed network o f nodes

* net-p2p/bittorrent-stats
Latest version available: 3.2.1b-r4
Latest version installed: [ Not Installed ]
Size of downloaded files: 141 kB
Homepage: http://bitconjurer.org/BitTorrent
Description: BitTorrent is a tool for distributing files via a distributed network o f nodes

* net-p2p/bittorrent-theshadow [ Masked ]
Latest version available: 5.8.7
Latest version installed: [ Not Installed ]
Size of downloaded files: 141 kB
Homepage: http://bt.degreez.net/
Description: TheShad0w's experimental BitTorrent client

Of course that isn't to say you could go to freshmeat or just do a google search and download a bit torrent client from somewhere else. You don't have to use only Gentoo provided packages.

yes, it should work.
you could get it through emerge, or install from source.

just do "emerge bittorrent" followed by "etc-update"

bittorrent will then be configured to automatically catch .bittorrent links in your browser

emerge doesn't work. It says that there is no profile directory system mode unavailable

doesn't work for bittorrent, or doesn't work in general? Maybe you should ask at forums.gentoo.org, since they probably know more about emerge.
If you just want bittorrent to work, you can download the source fom the official site and compile it yourself.