There's two parts at play here. First, there's the transmission of your message to whatever service you are using to send your SMS. Almost all of these use HTTPS, so it's already encrypted and not your problem.
The other part, and the one I'm guessing that you really are asking, is if there is a way to send encrypted data to a user that they don't need anything special to decrypt. Short answer is "No, unless the phone has software to decrypt if for you in their SMS app." I'm not aware of any phone that will do this for you today. All solutions I can think of require your user to access a service off the phone to decrypt their message, but the message could either be stored only on their phone in the SMS or on the service off the phone. Both could use a URL sent to the user that takes them to your off-phone service to decrypt or retrieve your message.