It's possible, but not that great of an option. One of the only ways you're going to make money uploading torrents & sharing the links on some site that you don't own, however, is if you figure out a way to monetize the torrent's contents. People have tried this for ages & I'm highly doubting that it paid off. If you create links to a site you own where you can make money & place those links / shortcuts, etc in a torrent, you may get some traffic (probably quite little), but trying to monetize something where your target audience goes out of their way to avoid paying for something, even to the extent of breaking the law.... that's not a good setup for profit. Especially with the increased scrutiny of torrents.
Aside from trying to monetize the content of the torrents, the only other way I can think of where an uploader could make money if they don't have their own site is to hide the torrent download links behind a monetized redirect service like adf.ly. However, I personally hate those links, only click them if I think the poster's cause is worth supportin & you need *a lot* of clicks just to make a couple of dollars. I believe you get a small fraction of a penny per click, possibly less depending on the location of the clicker.