Sending a text message from my Pi 3 to my cell phone

 DJackman  Depending upon how far the coop is from your WiFi, you could use ifttt.com.  They still have a free version.

Look at https://www.circuitbasics.com/how-to-send-a-text-message-with-ifttt/ for an example.

There are also numerous projects here on e14 that do what you're talking about.  Search "mailbox" and you will get a bunch of choices on IoT mailboxes - that notify the owner when the mailbox has been opened.  Not a very far stretch to a coop door. 

Personally, I would just use a messaging service like Telegram. I find this approach much easier, and it's free to use!

By way of examples, here's an element14 project which helps explain some of the basics through a project implementation:

 Telegram Controlled Drone #3 : Preparation - Telegram Bot

And here's random example found on Hackster.io: https://www.hackster.io/Salmanfarisvp/telegram-bot-with-raspberry-pi-f373da

probably some USB cellular modem (or a shield with something like SIM800) can be configured to send an SMS using AT commands - but it would require having a SIM card and some sort of  agreement  (with can be more or less expensive depending on location).

There were/are some versions of OrangePI with GSM modem built-in, for example:

http://www.orangepi.org/orangepiwiki/index.php/Orange_Pi_2G-IoT

which even includes documentation section about sending an SMS.

I personally own an (second hand) Orange Pi 2G, but have never used it - bought it cheaply out of interest but it is still waiting for a purpose, so I don't have first-hand experience about it.

BTW. I think that for the project you have described, something like Arduino with serial connected GSM modem could be sufficient (also probably more robust [no failure prone SD cards] and energy-efficient)...

Something like this? - just use any browser to control your door using your Pi...

https://www.youtube.com/watch?v=owgRkU_-4lw&ab_channel=SoftwareSage

Using cellular for your use-case is pretty old-fashioned. Nowadays, it may be worth investigating either LoRa, or LoRaWAN. The former is free,the latter can be free.

LoRa and LoRaWAN are popular for farm use, and for some scenarios where control or monitoring needs to occur over distances of a few miles to the nearest location with Internet (and from there of course, the control or monitoring can occur worldwide if needed). You'd have to google these topics, because there are many options, some DIY, some ready-made.

I actually came across this the other day, as I was looking at IFTTT for something similar. Looks like you can only use the Webhooks API with the IFTTT pro (paid) version.

A few probing questions.

Confirm the chicken coop Pi (ccP) is in the coop?

What network access does the ccP have? i.e. wired network, home wifi, it is an access point or none.

Are you expecting the ccP to deliver messages to the phone anywhere, anytime and anyplace?

Are you expect SMS text as the message protocol?

I personally don't get joy out of the "have you tried this method of problem solving." or "do it this way" just ignoring my initial attempt. I have kludged together solutions with Pi's. I like to help see if anything I have works.

Thanks for all the replay's.  I will look into them, to see what I can figure out. The weather nice so I've been working outside. Not much time on the computer. As the saying goes with farming "Gota make hay when the sun's shinning" Thanks i will get back with you guys and let you know what I figure out. 

Sorry working all the time. My coop Pi has wireless home WIFI and I would like to be able to receive a message no matter where I'm at. Even if I'm not home I would like to receive a confirmation that the door is open or shut. Don't really care what kind of message just SMS text seemed to be simple at first. Thanks D'Jackman