Would a tiger kill and eat a domestic cat?

Yes, a tiger would kill and eat a domestic cat if the opportunity presented itself. Tigers are opportunistic hunters and will attack almost anything even frogs, fish and elephants and all animals in between. Their prey animals includes domestic animals such as cows and buffalos. 

Sumatran tiger by Brookshaw photography.

There are records of tigers killing and eating another big cat, the leopard and a medium-sized cat the lynx. Tigers also kill and eat bears, wolves and foxes, all carnivores. Leopards avoid tigers for obvious reasons.

There is no gentlemen's agreement between the various cat species that they should not attack and eat each other. It would be nice if there was.

My source material is page 349 of Wild Cats of the World by the Sunquists. It is the best book on the wild cats in my view except it could do with being updated on conservation as it is dated 2002. There is relentlesss pressure on the tiger from human population growth and above all Chinese traditional medicine. Yes, I have to harp on about that ancient medicine based on superstition which is causing such great persecution of many wild species.