I was always told that you can’t but my Missus claims she got a sunburn through glass on a long journey across the US Midwest.
Thanks,
An Gadaí
Sure you can.
Most auto glass is tinted enough to keep the UV rays to a minimum.
Easily. I once burned the snot out of my arm and part of my leg on a long drive up the Sierras at altitude. All of it through the side window glass.
No matter how much time I spend in the sun nor how red I burn, I never get snot from my arms or legs.
freak
You just aren’t trying hard enough! 
(I’m glad I didn’t go with the first expression I thought of.)
You most definitely can. After a few days of riding the bus back home with a window to my right, my right arm was noticeably more tanned.
I see the OP’s location is Dublin… I wonder if this phenomenon not known or considerably lessened at higher latitudes? Because the “trucker tan” is well known enough in the States to become slang. (Trucker tan = a pronounced tan on the left arm, which would be near the window of the driver’s side of American vehicles.)
yeppers. i used to wear rings on both hands. during an 18-hour road trip from indianpolis to coral gables, i developed tan lines on my hands right thru the supposedly uv-resistant t-tops in the then-boyfriend’s trans am.
I think glass is like an SPF 20 or somthing- so not easy but possible.
I work for one of the largest automotive glass suppliers in the US. The glass is treated to resist UV, but does not block 100% UV. For instance, photochromic eyewear (activated by UV) will darken slightly in a car, but never completely. You’d have to be in the car a very long time or be very prone to burning, but I would say it is not impossible.
I always understood that the classic “trucker tan” was due to drivers hanging the left arm out the open window. (obviously no UV protection that way)
My left arm is noticeably darker than my right arm. Since I don’t sit in the sun with my right arm covered, I can only assume this is due to sun through my vehicle window.
Feynmann, in one of his books, claimed that he was one of the few people to see the first Trinity atom bomb tests with his own eyesight by watching the test through the glass in a truck cab, as he knew glass blocked UV rays. Was Feynmann lying?
An internet and print columnist of some repute around here has addressed this question.