I'm creating a website that requires user to sign up in order to get an account.I was just wondering, what type of api/code/etc do I need to use to send a verification code to directly to their phones.Once they receive the message they should be able to send like a text to that number (ex: send yes to confirm to the number #987) and the account automatically gets confirm from the text message.
Here you've got a list of SMS APIs: http://blog.mashape.com/list-of-50-sms-apis/. It's from 2013 though, some of them might have changed. You do have free APIs like http://textbelt.com/ but it depends on where do you want to send those SMSem, different providers in different countries have different gateways. I think it's impossible to answer you in 1 sentence.