IPA: /ɪnˈvaɪtə/
KK: /ɪnˈvaɪtər/
A person who asks someone to come to an event or gathering.
She is the inviter for the party this weekend.
Inviter is formed from "in-" (meaning into) and "viter" (from Latin "invitatio", meaning to invite). The word refers to someone who brings others into an event or gathering, hence an inviter is a person who invites.
Think of someone bringing others 'into' ('in-') an event — that's why an inviter is someone who invites.