Might be doable I guess. You would have to save a PGP pub key in your profile info somewhere (which could be publicly visible or not) and the system would use it do encrypt the message.
For decryption you would need to paste/type the priv key yourself each time (not really a fan of saving priv keys in DBs. Privacy usually comes with less confort)

You would need to trust that the priv key is not stored and only used to decrypt.
So trust your PMs are not read or trust your priv keys are no stored or trust that...

There's no such thing as a trustless automated system. Pluses and minuses I guess