Carrie Fisher's gravesite is calm and peaceful on Star Wars Day ... but her force is starting to draw fans who want to honor the galaxy's Princess.

Princess Leia's headstone -- shared with her mom, Debbie Reynolds -- was already adorned with flowers, cards and a 'Star Wars' gift bag early Thursday morning. Many more are expected to arrive throughout May the Fourth.

No lightsaber fights breaking out yet, but it's early.

Carrie and Debbie's shared huge headstone was placed over their graves earlier this week at Hollywood's Forest Lawn Cemetery.

Yes, the Fourth is strong with this one. And also with this musical tribute to Leia ...