If you are going to the SMS route you don't actually need to store the Phone Number. Instead, you can store a Hash of the Phone Number, this way you can still check whether the Number has been used before without needing to store it. Though of course is pre supposed a certain level of trust in you. It's mostly to your own advantage if for example a government comes asking for that data you can honestly answer that you don't have it.
Really bad idea imho, there are only a relatively small number of phone numbers possible so it would be relatively easy to brute force a simple hash. Not sure beyond that though, the hashes re-hashed with another key would work but would put all the trust on the key holder, needs someone with crypto knowhow.