Things I try that I know work:
Put them in such a way that they do not wrap around the spinning portion of the washer. This can be done by putting heavier clothing in with it or washing it by itself.
Try putting your washer on a gentler setting. This can stop the washer from twisting the clothing.
Pulling the sleeves inside the shirt and tying the sleeves in a bow also work.
Fold them and tie them with something or put them in a delicates bag. This will stop the clothes from twisting because they will have absolutely no interaction with the washer.
If I am understanding your problem correctly then this comment on fluther.com will help:
From the user Wildflower:
It’s a matter of quality of the fabric – and is often indicated by the
price. I think low-cost logo’d shirts are more likely to do this. Some
t-shirts are made from stretched or loosely woven/knitted cotton and
it may lose it’s shape. Others are made from good quality cotton, but
not cut straight (in line with the fibers) and they may ‘warp’ too.
The best way to avoid it is to dry them flat so that you can shape
them while still wet and let them dry that way.
Some shirts are very prone to wrinkles this being, because the fabric is a gentler fabric. Washing and drying by hand is a good solution. Heavier fabrics cannot twist as easily.
Things that may not be a solution:
My sleeves have not twisted in a long time, I think this may be because:
Reddit seemed to have a lot of the same ideas with additional ones.
Dryer Balls. Tennis Balls work just as fine, but some people say they damage your dryer.
Try shaking them out before putting them in the washer. From experience shirts are more likely to become crinkled if they are left in a ball or not totally unfolded.
Don't overload the washer. But I think overloading it can stop the clothing from moving in such a way that twists them.