"Mesmerize" is a verb.

To Mesmerize is to hypnotize, to fascinate, or to compel by fascination.

Mesmerize - video game - happened in 2007.

Mesmerize - song - was created on 2002-12-16.

this question can be a bit subjective because this is more depending on how the person get mesmerize by you instead of your mesmerize him. so if you want to mesmerize a person,understand that person and eventually the thing you do will mesmerize him/her as you will act according to that person preference.good luck