It is surprising that after a considerable amount of research through many books that I have on cats including wild cats and on the Internet (and I’m a good Internet researcher) I cannot find clear, definitive information that tigers can have identical twins. This does not necessarily mean that they can’t. It just means that there is little interest in it and even less research. It is also probably vanishingly rare and it may never happen. I would be pleased to hear from people better qualified than me on the topic in a comment.
My distinct impression is that tigers, being mammals can have identical twins, at least theoretically, and very rarely. They can certainly have non-identical twins as can many other animals. But I cannot find any hard factual evidence of identical twins being born to tigers. There are no studies on it example.
The nearest I got to evidence of identical twins cats is a story from the American Kennel Club about dogs having identical twins. These are Irish wolfhounds in South Africa and scientists were able to perform a DNA test which confirms that the brothers were genetically identical (2016). Obviously dogs are not cats but they are both mammals and therefore I’d argue that all species of cat including tigers could have identical twins under certain circumstances.
There is one animal at least, which is the armadillo, which produces identical quadruplets resulting from to binary visions of a single fertilised oocyte (Quora.com).
For the record, the Wikipedia authors say that twins are common in many mammal species including cats. They do not refer to identical twins which as you know is the result of the fertilisation of a single egg to form one zygote which then divides into two separate embryos. This is in comparison to fraternal twins (dizygotic twins) which occur when two fertilised eggs are implanted in the uterus wall at the same time and are independently fertilised by two different sperm cells.
I’m sorry that I’m not able to produce conclusive evidence of identical twins in tigers. As I said it surprises me that there is not more information on identical twins in animals in general. There’s a video on the Internet from BBC Earth about twin tiger cubs. I presume these are non-identical twins. Although this is not specified. The video is below and the picture at the top of the page is a screenshot.