Can't enter sign-in verification number on my iPhone

I just changed phones. I'm being asked to enter all of my ID stuff. On my phone, I'm asked to enter the sign-in verification code sent to my email address. I've gotten the verification code, but when I go to enter it on my phone, the screen does not have a pop-up keyboard, so there's no way to enter the code. And I can't get past it. This is ridiculous! How do I solve this problem?