A lot of people don’t seem to know about this setting, but it’s pretty useful, especially if you’re running an account for a brand or if you want to give everyone an ability to privately message you without having to follow them or giving out your email address in public.
Head to the Twitter settings page and about halfway down the Account page (the first settings page you’ll land on), you’ll see the following:
Check that box…that’s it! As long as the other person follows you, then you can have a conversation via DM.
Edit: Apologies to everyone wondering why this wasn’t showing in their settings – apparently this was a feature that Twitter removed for some users shortly after implementing it but because it showed in all of my Twitter account settings (I have quite a few accounts) and it still works for me, I assumed it was still a thing. Sorry everyone! Boo Twitter!