Rory McIlroy -- I'M ENGAGED ... Again!

Just a year-and-a-half after breaking off his last engagement, Rory McIlroy is trying it again -- popping the question to his NEW girlfriend Erica Stoll ... and she said, "Yes."

The couple hit the red carpet together at a charity event in Ireland Thursday night -- after reportedly putting an engagement ring on it during a romantic weekend in Paris.

Clearly, Stoll is hoping this engagement goes better than Rory's last one -- in which he broke up with tennis superstar Caroline Wozniacki OVER THE PHONE after they sent out their wedding invitations.

Wozniacki has been connected to a few different guys since the split -- including JJ Watt and David Lee.