How do I block a specific phone number from calling or texting me?
I think saying that it's possible without elaborating is just as helpful as not replying at all. OP probably already knows he can but wants to know how. I'll elaborate on what Dennis said. If you go into a text message with that number, or look them up through your call logs, hit then menu/options button (or it might be 3 dots in the corner of your screen) on your android and a menu should come up that has an option that says "Add to reject list". Click that.
No dice so far, but thanks for replying. If I click on a number through my call log all the menu (or three dots) gives me is the option to Place On Home Screen. I have even tried going into the android default Messaging App but all it gives me are options for Messaging, not the contact/number themselves.