。
A student's job is to study.
Literal
Study [nominalizer-こと] [subject-が] student [gen-の] job is (polite).
An aphoristic claim using こと to nominalize 'studying' as the subject of 仕事 ('job/work') — 'studying is a student's job.' こと feels slightly more formal or abstract than の as a nominalizer. 仕事 is more everyday than 務め ('duty') or 本分 ('proper calling'), but still carries the implication of responsibility.