You would also need the torrent's hash (which enable you to specify to the tracker which files you want exactly). That's how magnet link [1] works - they contain the torrent's hash and optionally a list of trackers (most clients today support DHT [2], a decentralized tracker-less way to find peers).

[1] https://en.wikipedia.org/wiki/Magnet_URI_scheme

[2] https://en.wikipedia.org/wiki/Distributed_hash_table

I made a few simplifications for brevity and "these files" was one of them. What the .torrent actually contains is a list of the files and how those files are divided up into chunks of equal size (say half a megabyte per chunk). The bulk of the torrent is a list of hashes of each chunk, which allows your client to verify the data it has received from other peers. If you then take a hash of <<the part of the torrent that lists the files and the chunk hashes>> the resulting hash is known as the infohash. The infohash describes this particular torrent uniquely, and it's the infohash you send to the tracker when asking for peers.

Hopefully from this explanation you can see that you need it for two purposes, one so you can give the right infohash to the tracker, and two so you can verify the data you receive from peers.