Cat got your tongue?
A question addressed to someone who is inexplicably silent.
'Cat got your tongue?' is the shortened form of the query 'Has the cat got your tongue?' and it is the short form that is more often used. It is somewhat archaic now but was in common use until the 1960/70s. It was directed at anyone who was quiet when they were expected to speak, and often to children who were being suspiciously unobtrusive.
There's no derivation that involves any actual cat or celebrated incident of feline theft. It certainly doesn't relate to sailors becoming taciturn when punished with the cat o' nine tails as some have suggested - that's pure invention. Like the blackbird that 'pecked off his nose', the phrase is just an example of the lighthearted imagery that is, or was, directed at children.
The expression sounds as though it might be old but isn't especially so. It isn't found in print until 1881, in the US illustrated paper Ballou's Monthly Magazine, Volume 53:
Has the cat got your tongue, as the children say?
The demarcation of the phrase as being 'children's' suggests that it may be earlier than the 1880s. Children's language wasn't written down until it became used by adults, which may be some years after it was common parlance in the playground.