What happens when you click on that button? Can you share the url to that page?
If the button just opens up a regular form where the visitor can type in some info, then you could simply use a regular webform and instead of sending to your email address, have it sent to your mobile carrier's email to text address. Pretty much all of the mobile networks have an email address that can be used to send an sms/mms message to your phone. Verizon for example uses the following format:
Here's a link that shows the format for most networks: SMS Gateway: From Email to SMS Text Message
I appreciate this, thanks. So there is no wordpress plugin that does this? Thats surprising (shrug)!The way they are achieving this is by using html markup, similar to when a webpage has a phone number that you can click to call, or an email address that you can click on and it opens your email app. If you have someone that helps with your website, it should take just a few minutes. If you maintain your own website, it is still very doable. Here is a website that can walk you thru it: How to Create HTML SMS Links | SimpleTexting