Our tortie does this with toy mice. We always know she’s coming with one because we can hear her meowing as she carries it.
Once we were almost presented with a real mouse she had caught in the back yard. We decided she could stay outside for just a bit longer that evening...
Mine had a cat door. One day I took a nap on the white wall-to-wall carpet and she, presumably, went out. I was barely awakened a half hour later by a tiny little meow. I opened my eyes without moving, and there was a bloody dead field mouse between me and her smiling face.