▲根据《新汉英大辞典》：

“学生会”可用 student union; student association; student council 等来表达。

▲高考英语试卷中 student union 和 students' union 的表达都出现过。如：

In order to make the best of learning materials, the Students' Union of our school is  arranging an activity.(2007高考英语福建卷)

I'm Li Hua, Chair of the Student Union of Yucai Middle School, which is close to your  University. (2010高考英语全国卷Ⅰ)