The site lets you create an event, and then invite people:

Or you can send them the link and they can join themselves. Everyone who is a member of the event will get an email reminder prompting them to RSVP, a few days before each event:

From: Regularly Scheduled <jeff@jefftk.com>
Subject: Reminder: Demonstration Event
         is this Tuesday; rsvp?

Demonstration Event is this Tuesday.  RSVP:

    https://www.regularlyscheduled.com
       /event/jCafDI6yAiny/2017-08-22?id=...

Which takes you to a page where you can RSVP, and leave a comment if you want to:

The overall goal is to be very light-weight, just something to handle reminding people about the recurring event and collecting RSVPs. Kind of like Doodle is for scheduling one-off events.

This is still very beta, I've only just made it [2], and it might not work. But maybe play with it and let me know what you think?

(Why not Google Calendar? Not everyone uses it, it doesn't remind people to RSVP, and the interface is too general to do a good job for this specific use.)

[1] I have three regularly scheduled gatherings: dinner with my extended family on Tuesdays, the local contra dance on 1st and 3rd Sundays, and a dinner with friends from college on 1st Mondays and 3rd Thursdays. All of these get me to remember to do a kind of thing I want to be part of my life and enjoy when I'm doing it, but might not otherwise remember to schedule.

[2] The code is on github. I wrote it quickly, and it's not especially good code.