I can't for the life of me figure out how to send an invitation to connect using the iPhone app for LinkedIn. Is it not possible? I'm using iOS 6.0 and LinkedIn's app version 5.1.
One way to invite a new connection is to open that person's profile (either via person search or viewing someone else's connections). Once that profile is open, click on the blue "Invite to Connect" button underneath the profile picture.
Example image (courtesy of stayingaliveuk.com):