"Can I have a glass of juice?" 或 "Can I get a glass of juice?" 是拿一杯果汁的常用表达方式。
"Can I have" 或 "Can I get" 都是询问得到某物的常用语。"Glass of" 是固定用法，表示一杯，后面接上所需要的饮料，如"juice"。
例句:
Can I have a glass of orange juice? (我能喝一杯橙汁吗？)
Can I get a glass of apple juice? (我能喝一杯苹果汁吗？)
Can I have a glass of cranberry juice? (我能喝一杯蔓越梅汁吗？)