"Small dogs, cats and household birds can travel in the cabin for a one-way fee, collected at check-in. They must be able to fit in a small, ventilated pet carrier that fits under the seat in front of you."
"Your pet must remain inside the kennel (with door secured) while in a Delta boarding area (during boarding and deplaning), a Delta airport lounge and while onboard the aircraft."
Edit: can be a service animal