If you search the plugins directory for SMS, There are a few plugins that might help if you ignore the ‘SMS mailing list’ ones: http://wordpress.org/plugins/search.php?q=sms
This is something I do very often with contact forms on websites. All or most phone companies provide an e-mail to text service. Here is a link with the list of email addresses that send a text. The e-mail address usually starts with your 10 digit phone number. Verizon for example is 10digitphonenumber@vtext.com. The problem to look out for is the 180 character limit can cause important information to be lost. You can set-up and test your contact form so that it is concise, sends the most important fields first and add a character limit & warning to your form. The message character limit will in practice be way less than 180 because the contact form will send some xtra information in the text. I usually specify that the user put their contact information in the subject line so that info is sure to get through! As a backup I setup the contact form to send me BOTH an e-mail text and a regular e-mail. That way any overflow message is not lost and can be accessed. Contact Form 7 works well for this! Hope this helps.