"solicit to come," 1530s, a back-formation from invitation, or else from Middle French inviter (15c.), from Latin invitare "to invite," also "to summon, challenge; to feast, to entertain," a word of uncertain origin. Related: Invited; inviting.
"an invitation," 1650s, from invite (v.).
Can I invite you for dinner on Sunday night?
I invited them to a restaurant
We invited the neighbors in for a cup of coffee
The organizers invite submissions of papers for the conference
he didn't get no invite to the party