If you’re talking about creating a link, which when pushed on an iPhone, opens the Messages app to send an SMS, then all you need to do is make a URL like this:
sms:2155551212
The iPhone will open Messages and set it to send a message to that number.
If you want to have a text box on your page which can send an SMS, then that’s a much different and more complex kettle of fish, not easily solved without throwing money at the problem.
Is there a way to have the sms link open the user’s messaging app on his DESKTOP like what would occur with mailto: (opening the email app) or even tel: (opening Facetime)? It works on my iPhone, but on my desktop it tries to open the page sms:111-111-1111.
Try it without the hyphens but certainly in Safari on a Mac Messages is not recognised as a Recommended app to work with an sms link. There may be one but the User would have to have configured it themselves for it to work.
So the short answer is no - not without the user setting it up.