That's the same problem I had with my Samsung Android phone. I just downloaded GO SMS Pro from Google Play. With the app, you can use custom ringtones for your incoming text messages. You can even assign a different tone for each contact.
In this case try going to Menu——Options——Ringtone--Select phone ringtone(open the ringtone list to choose the ringtone)/Select from music(open the music directory to choose the ringtone ).
Follow the link below.. It's the easiest way to do that..