Rory Culkin's officially a father ... with his girlfriend Kate Arizmendi announcing the birth of their first child on Instagram.

Arizmendi shared a pic of their newborn daughter sleeping ... hands curled up under her chin as she rests.

Arizmendi revealed their daughter's name on the photo ... calling her Havoc Moon. She was born on Saturday -- and Kate says she and Rory love her deeply.

Rory and Kate -- a well-known cinematographer -- have been together since 2023. He was previously married to Sarah Scrivener, whom he met on the set of "Scream 4," but they have no kids together.

Kate announced she was pregnant earlier this year ... and their family threw them a baby shower earlier this month.

While this is Rory's first child, he's got a lot of practice with his nieces and nephews. His brothers -- Macaulay and Kieran Culkin -- have 2 and 3 kids, respectively ... and that's just counting his family members in the public eye.

Congrats!