Currently the only way to send an invite to a non-Matrix user is via email or via 'word of mouth'.
The problem is that when users don't join Matrix via that email link they often register on the wrong Matrix Home Server.
This is currently often the case with the mobile clients as users are registering via the Riot/Web and then installing the mobile and desktop clients.
I've had many users regiser via a web link then complain that the room is missing on the mobile client because they've re-registered at Matrix.org rather than logging in to a private home server using the registration they already created from an email link to Riot/Web.
Solution:
On Android and iOS you can register an action toa URL via the applications' manifest, using the 'intent-filter' and 'action' elements.
Also known as Deep Links or Android App Links
It would be trivial to do this for Riot/Android, RiotX and Riot/iOS, such that when an invite is sent it opens the app (or offers to install it) and then joins the correct room on the correct home server.
This could be useful as it work also work with URL sources other than text links, e.g. NFC and QR.