Hmf. Not if you phrase it as "ordering a drink." Apparently that's something you can do all by yourself.

[it makes no sense to him. With a gruff sigh, he stands and heads to the bar. He explains something to the bar tender and waits. With a glass in hand, he returns to Mikasa, and shoves it at her]

Here.

[it seems to be a glass full of crushed ice and some sort of red syrup. There's a strawberry on the rim and a long spoon for eating the ice with. Tasting it will reveal the flavor to be some sort of strawberry and raspberry puree, simple syrup, and the faintest trace of rum]

This is close to what we call a "sno-cone" in my world.