You wouldn't be able to just transfer them. You could email them to yourself from the old phone (over WiFi) and then get them on the new phone. Depending on the phone's options (most don't/can't do this), you 'may' be able to save the texts as files and then transfer them over to the new phone either (again) via email and WiFi or copying them over to a computer (via USB cord) and then moving those files over to the new device, again via USB connection.