The text is a play on the Miranda rights warning given by police in the United States, which includes the right to remain silent to avoid self-incrimination. However, the second part 'USE IT!' is an imperative, suggesting that the person should actually remain silent, possibly because they are talking too much. This does not exploit different meanings of a word or similar-sounding words for humorous effect.
You have the right to remain silent . . . . USE IT !