Bradford Cat Watch Rescue Kittens said it had taken in several of the animals which had been rescued by police.
They are coloured or dyed so that players who bet on a chosen kitten know which one has been killed first.
Sanctuary owner Katie Lloyd said: “This is not just a couple of idiots colouring in kittens. This is serious barbaric cruelty. “If these kittens were not rescued I am sure they would have been dead within an hour of two.”
The kittens were rescued by police from a property in Bradford.
Ms Lloyd, a former paediatric nurse who has run her kitten rescue centre for ten years, received a call about the male kittens last night.
She said they were in a terrible state, they were shell-shocked, lethargic and had breathing difficulties.
One - named Smurf - was agitated by the marker pens and was itching severely.
Ms Lloyd said: “We whipped them straight to the vets. They are on medication and have eye drops, we are also bathing them in a special solution.
“So far they have had three baths overnight and one this morning (Tues). The colour is starting to come off their bodies, but is still on their faces and in their eyes.
“They are still quite poorly but are slowly getting better. We are giving them lots of care.”
The sanctuary has rescued around 5,000 cats and kittens in its 10 year history.
Ms Lloyd added: “We have sought veterinary advice and I have just contacted the poisons unit to ascertain what would be safe to use on them to try to remove the ink.
“The kitties are now going for a bath”.
The sanctuary is now appealing for help with the funds to care for the kittens.
The director of claims and marketing at Animal Friends insurance company, Wesley Pearson, said: “When a pet has a loving owner they quickly assimilate themselves and become a part of the family.
“For a loving owner, the bond between themselves and their pet is meaningful and reciprocal. So the idea that anyone would deliberately abuse an animal is simply awful.
“Beyond the discomfort and dangers associated with exposing these kittens to this experience, the suggestion of using them as bait for sport is horrifying.”