You can flip the button on the side of the phone to make it go to vibrate mode only but then all incoming calls, alarm notices, schedules, etc.. will also be on vibrate. Another option, if your phone is jailbroken, is to change the sound for the text to a blank mp3 so that it plays the sound but nothing is actually played and then the vibrate should be your only notice. The problem with that is that once changed it will stay that way forever until you change the sound file back. You wont be able to turn it on and off whenever you want.
This seemed like the best place to ask my question regarding texts and the alarm. If I put the phone on silence, does this also mean that this applies to both alarms and texts? I'd rather not deal with texts at 6 in the morning but at the same time, I need that alarm to be on. Thanks!