First of all, you have to appear for GATE Exam and score the qualifying marks to clear it. After this, you can apply to an internship or job at ONGC. You will have to appear for the interview where you will be judged on the basis of your B.Tech percentage, the category you are applying in and your GATE score. So, yes you can apply.

1.eligibility criteria
Eligibility is one of the most important part of any competitive examination. Be careful before applying for the exam and read all eligibility criteria carefully.

2. nationality:

A candidate must be citizen of India, Nepal, Bhutan, Tibetan Refugee who came over to India before January 1, 1962, person of Indian origin who has migrated from Pakistan, Sri Lanka, Burma, East African countries of Kenya, the United Republic of Tanzania (formerly Tanganyika & Zanzibar), Uganda, Zambia, Malawi, Ethiopia, Zaire and Vietnam with the intention of permanently settling in India.

3.qualification:

Candidate must have a bachelor degree, he/she required to secure a minimum of 60% marks in qualifying examination.

4.age limit:

Date of Birth as recorded in the Matriculation / Secondary Examination Certificate only will be accepted by the Commission for determining the age.