Yes, they can but not because of an emotional reaction to something but as a physical means to wash away a substance on the cornea of their eye or eyes.
The point is this: the dictionary definition of crying is “to shed tears, ESPECIALLY AS A RESULT OF STRONG EMOTION such as grief, sorrow, pain or joy.
The key phrase is in capitals. It strongly implies that crying can be for reasons other than an emotional response.
On that basis, as mentioned, tigers can cry because occasionally their eyes will water up because of a range of physical reasons such as dust in their eyes.
THERE ARE SOME PAGES ON FELINE EMOTIONS AT THE BASE OF THE PAGE.
I am not saying that it happens a lot but it must happen occasionally. Also tigers have tear ducts which means they have the anatomy to create tears. Tear ducts drain the tears from the eye to the nose. All cats, domestic and wild have them.
If they can produce tears they can cry. It is just a question of deciding for what reason. It won’t be because of an emotion.
That said I am applying logic. There are no scientific articles on this topic. No scientists have spend days and weeks studying the tearing mechanism of tigers and deciding if they feel grief.
Feline emotions by the way is work in progress for humans. With respect to the domestic cat scientists are still figuring out if cats can experience the higher emotions like grief. There is a debate about it.