If you're running a web server, why not just put up a page with a "ring" button and bookmark that on your phone?

Just make sure it isn't a GET, per a discussion the other week...

Or if you wanted to get even cheaper, depending on the carrier, you could text a personal E-Mail server.

Expose your server endpoint to the public web however you like. There are lots of options and many have been discussed here recently. I just happen to be a fan of ngrok and use it daily for all sorts of cases, including on some of my Pi’s.

Does it work well over extended periods of time like that? I’ve just thought of using it temporarily for testing.

I have a tunnel that’s been running for over a month now with no issues. Basic free tunnels do have an expiration (24 hours IIRC) but the paid accounts will let you keep a tunnel open as long as you want.