Of course - but it seems a little juvenile nowadays. Calling shotgun was something we did as high school teens.
I heard this a year or so back and had to ask one of the (harumph) young people who I work with what it meant.
I’ve known it for as long as I can remember, but don’t recall anyone using it in real life (UK).
Heard it all my life in the UK.
Never heard it in my 37 years in the UK. Came across it maybe 5 years ago when my mostly-US-raised kids started saying it.
Remember that from a kid - if my mum was not in the car me and my brother - sometimes even my sisters would shout ‘Shotgun’ - not riding or calling just ‘Shotgun’
(UK)
I remember “shotgun” being called in the late 1940s and it was certainly common in the 1950s, at least back home in Texas. I think I remember hearing it a few times in California during the 1960s but I can’t be entirely certain about that.
I’m the OP’s mother’s age, and I first heard it in California in the early '70s.
Once, when headed out for some skeet shooting with friends, I actually called “shotgun” while I was holding one. Everyone cracked up and one guy quipped that holding a 12-guage entitled the bearer to sit wherever he wanted. 
Justlike this!
Very true. If you’re all sitting around the dinner table and somebody says “Let’s all go out for ice cream later,” and you yell “Shotgun!,” you’re just a loser. Total L7. You have to wait till you’re on the way to the car and hope everybody else forgot and you can see the :smack: on their faces because YOU CALLED IT!
Australian, heard of it, didn’t know the exact meaning. The correct term is bags e.g. “Bags the front seat”
Well, moms don’t have to call shotgun. In fact, if your mom is going somehwere with you the shotgun calling has no effect until it is clear where she will be sitting. If, for example, you, your two brothers and your mom approach the car and mom announces “I will ride in the back” then, and only then, can one of the other passengers call shotgun. And that can be canceled by mom at any time. So it seems resonable to me that your mom never heard the phrase.
Another fellow who’d heard it as a kid since the 1960’s.
I wonder, do people living in shotgun shacks ever call “Shotgun!”?
I know it and have used it for as long as I’ve been riding in front seats.
These days, I’m usually in the driver’s seat so I don’t get to call it very often.
Just “shotgun” around here. My kids also ocassionally call “shotgun shell” (behind the shotgun) - since we’re all tall, the driver gets to position the seat comfortably, but the front passenger needs to pull up enough to let the guy behind him at least get his knees in (more of an issue with compact cars).
There are apparently rules (somewhat amorphous but in line with what has been expressed above) - but as Dad, I get to sit where I want (usually behind the steering wheel).
I never even had siblings and I still know what it means.
I’m 45 and I’ve heard and used this all my life. Of course, there are rules. On How I Met Your Mother, Barney tried to call infinity shotgun in Ted’s new car, and we all know that’s not allowed!
Kids these days probably won’t learn shotgun as early due to the required sitting in back until they are older.
I know what it means but I don’t use it on a regular basis. Instead, I use “I call front!” (since I get motion sick and riding up front helps.
I also from time to time call out: “I get first shower!” (after camping or a long car drive)