Well there are a plenty of services available. All of them paid. They do offer a trial version with limited api requests.
You should note that the way to figure out which carrier a number belongs to will be country-specific.
The information is, at least there, not available to the public - I've known service providers, network operators and information providers (as in yellow pages) that have access.
But, wouldn't a proper sms gateway service do this for you?
The cheap ones out there you could try out are
1) Data24-7 offers an API for looking up the carrier for wireless phone numbers. It also returns the email addresses to send SMS and MMS messages to the phone. It's not free, it's $12 per month and $0.006 per lookup. Check it out on
http://www.data24-7.com/carrier24-7.php
2) Twilio is one of the most reliable service provider out there.
You can find some more providers here https://git.daplie.com/coolaj86/node-tel-carrier