Meeting Invite Iphone
You can't directly send an invite via text message with the stock iOS calendar. 

However, you can send an invite to the email address of their mobile device.  For instance, if I want to send a calendar invite to someone who has an AT&amp;T mobile number, I can send it to their number @txt.att.net.  

This will be seen as an email address by Calendar and you can send it out. The person receiving it will get it as a text message.  Depending on their mobile network provider, they'll be able to accept to decline the invite.  

Of course, this requires you to know the mobile network of the people you wish to invite so it isn't perfect. There might also be 3rd-party apps on the App Store that can provide the service you're looking for but I don't have any names offhand.