From Chipotle's web-site, I can see they were giving away free burritos. This was apparently due to them being closed for staff meetings on February 8th.
Is it a real offer?
Yes. Time confirmed this and wrote a story about it:
All you have to do to redeem this offer is text the word “raincheck” to 888-222. They’ll text you back with a coupon for a free burrito within the next few days.
The page cited in the question linked to the Offical Rules which clarifies about your phone charge concerns:
NO PURCHASE OR PAYMENT OF ANY KIND IS NECESSARY TO PARTICIPATE.
There does not appear to be any hidden charges, beyond the normal fees required to operate a device that can send a text, receive an image and display a QR code.
I'm not sure if this is entirely appropriate given the posting guidelines say "Avoid statements based solely on ... personal experience;", however, I don't think those were written with this specific situation in mind (also I cannot comment, as I do not have an account).
In case you hadn't guessed, I personally got a free burrito. I went there for lunch on Feb. 8th, 2016 at about 12:30pm and there was a sign on the door similar to the one in the question. I texted the number as directed, they sent me a link to their website where I was required to enter my name, phone number, and zip code.
The next day I received a text saying "Here it is. Ur free burrito." and a link to a site with a QR code. I went to chipotle the next day (wed. the 10th), showed the cashier the QR code on my phone, she scanned it, and I got a free burrito. To be perfectly clear, the only thing I got was a burrtio (with extra steak, even) and was not charged anything (ie. I did not give they my credit card or any money). I did not incur any texting fees as I have unlimited texting with my phone plan.
I'm not entirely sure why you are skeptical of this, considering the link you posted is from Chiptole's official site... Regardless, it is/was a legitimate offer.
And they say there is no such thing as a free lunch.