I was always taught that Esquire was an honorific, and it was bad etiquette to refer to oneself as such.
Law Encyclopedia: Esq.
This entry contains information applicable to United States law only.
An abbreviation for esquire, which is a title used by attorneys in the United States. The term esquire has a different meaning in English law. It is used to signify a title of dignity, which ranks above gentleman and directly below knight.
In the United States, Esq. is written after a lawyer’s name, for example: John Smith, Esq.