The degree written in the recruitment is undergraduate, so can I take the undergraduate exam myself?

Yes, it's better to write clearly that it is a self-taught undergraduate course.

Self-taught undergraduate examination is one of the basic systems of higher education in China. The effectiveness of the self-taught diploma is related to the degree of personal efforts. After passing the examination, the examiners' school and the higher education self-study examination committee will jointly issue the university graduation certificate. Education is recognized by the state and can be found on the learning website. Those who meet the requirements will be awarded a bachelor's degree by the examiner university.