Without having the torrent software installed? AFAIK there's no web-based bittorrent client, but not all of the clients that do exist require admin rights to install... try Azureus (http://azureus.sourceforge.net/) or uTorrent (http://www.utorrent.com/), those are some of my favorites - not sure if they require admin rights to install but you could try...
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The Ed draws near! What dost thou deaux?
utorrent doesn't even really install. Just tell it NO when it asks to if you want to associate it with torrents.
That said, if you don't have admin I wouldn't be using torrents without getting permission first. Set up wrong they are very noticeable and leech a lot of bandwidth. Neither is likely to make the IT department happy with you.
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Phoenix-D
I am not senile. I just talk to myself because the rest of you don't provide adequate conversation.
-Digger
You could use the Opera webbrowser aswell, since it has torrent support.
Or if you are using Firefox, there is an extension that allows downloading of torrents inside the browser.
Else µTorrent is the best choice since you can just start it and it will download things for you. And since it is such a lightweight but powerful client it would be my first choice.