.
Edit: I got a glimpse of the channel that time before it kicked me out asking for a phone number, so it seems that I've written above is indeed the case. Shame we couldn't use something a bit more privacy respecting like Riot. I also won't be signing up if it requires a phone number or a clearnet connection.
It can be certainly used via a VPN as many of us are using them. So that could be a compromise if you're willing to do so. Failing that, you could potentially create an account on a VPN connection, and then try using that account as normal on a Tor circuit. I'm not sure whether Discord will still ping you, but I'm assuming they just don't like "dirty" connections upon signing up, and once that process has been done it wont bother you much. That's my assumption anyway.