The simple answer is yes but no offence you are probably not ready for it yet as your question implies that you don't yet know what a .torrent file is - i.e it doesn't contain the files you wish to download, it just holds data that tells BitTorrent clients where to find the files you wish to download.
There are online BitTorrent clients that will do the downloading for you then host downloaded files for you to then access, but I have never used one so cannot recommend.
What other options you have will depend specifically on what it is you wish to do, for instance there are sites from which you can stream video or audio content, there are legal sites (i.e. paid) and illegal ones (i.e. free), the illegal ones tend to be rife with malware and intrusive advertising - access to illegal ones may be blocked from public computers but if not then don't worry too much about the malware as (with a total lack of social responsibility) it's somebody elses system! But they will probably ban you if they find out.