The television personality appeared in the new documentary, "Christianities?" ... where he revealed he'd once woken up to find huge claw marks on his sides and shoulder -- ones that didn't match his own hands.

Carlson says Satan's servant didn't wake his wife or dogs -- who TC says are notoriously light sleepers -- but, he had to go to the bathroom to see the damage the supposed demon had done.

When he flicked on the bathroom light, Carlson says he saw 4 claw marks on each side of his rib cage and more on the shoulder that were bleeding profusely ... markings he claims haven't gone away about 18 months later.

The next morning, Tucker says he thought the attack had all been a dream ... until he saw his blood-soaked sheets.

Carlson says the incident made him explore his faith, reading the Bible to figure out exactly what happened ... though he says he still doesn't understand it to this day.

Worth noting ... Tucker admits he was sleeping with 4 dogs in the bed -- so instead of a demon, a sleep-running puppy may have accidentally scratched him. That's one theory online, anyway.