Yes, a B.Sc Final year student is eligible to appear in IAS entrance. You need to appear in the Civil Service Examination which is conducted by the UPSC. Following are the details of this examination:

Required qualification:
The applicant should have completed graduation with good academic record from any recognized university of India, students appearing in the final year examination are also eligible for this examination…………..

Age Limits
Candidate must have attained the age of 21 years and must not have attained the age of 30 years on 1st August


Nationality:
A candidate must be a citizen of:
A citizen of India, or
A subject of Nepal, or
A subject of Bhutan, or
A Tibetan refugee who came over to India before 1st January, 1962 with the intention of permanently settling in India, or
a person of Indian origin who has migrated from Pakistan, Sri Lanka, Burma, East African countries of Kenya, Uganda, the United Republic of Tanzania, Zambia, Malawi, Zaire, Ethiopia and Vietnam with the intention of permanently settling in India.