The couple welcomed a son named Dakota Song Culkin, after the actor’s late sister, Dakota, who died in 2008 at the age of 29.
The baby was born in Los Angeles on April 5.
Culkin and Song met a few years ago on the set of “Changeland”. They both had roles in the film.
Culkin is currently filming season 10 of “American Horror Story” with Sarah Paulson, Kathy Bates, Billie Lourd, Evan Peters, Lily Rabe and Finn Wittrock.