Somewhere near the bottom of the event editor, you should find settings relating to RSVPs:
It’s pretty straightforward, consisting of just two options and links to let you view confirmed attendances and absences.
Event Rocket does not assume that you wish to provide RSVP functionality for every event. Normally, then, you need to enable this by checking the relevant checkbox. Until you do this, users cannot confirm their attendance.
Restrict to logged in users
It’s entirely possible to let anonymous users RSVP to an event, but this setting is generally recommended and means only authenticated users will be able to RSVP.