Can I play at ACR as a UK-based player?

They don't seem to have a UKGC license, but nothing on the site tells me I can't sign up. I also see UK streamers playing there but maybe they are using a VPN or something?

I don't want to use any kind of "trick" to bypass the system to play there, but I'd sure like to give it a go if I'm allowed.

Yes you can play ACR from the UK, they don't have a UKGC licence as they aren't a regulated site, that doesn't mean they aren't a reputable site though.

As Martin say, you can play there. You just need to be aware, that withdrawals will be more complicated and/or expensive, than they are on the regulated sites. Check out the withdrawal options, before you deposit.