There are a lot of free messaging apps in the Play store, and some of them allow a signature. (Since texts aren't formatted, it's just text added to the end of what you send, there's no break bar or formatting, the way there is for signatures in emails.) Install some free ones, until you find one that allows signatures. (And uninstall the ones that don't - do them one at a time, install, then uninstall if that one doesn't allow signatures, so you don't fill the phone up with apps you're not going to use.)