Carter’s parents on Dutton Ranch are Beth Dutton and Rip Wheeler; he’s their adoptive son, not their biological child.

Quick Scoop

The show’s coverage consistently describes Carter that way, and recent recaps still refer to him as Beth and Rip’s son. So the simplest answer is: Beth and Rip.

Small nuance

If you mean biologically, the series has not presented them as his biological parents. If you mean in the family sense, they are his parents on the show.

TL;DR: Carter is Beth Dutton and Rip Wheeler’s adopted son.