Yes you can apply for Indian engineering service examination after passing ME degree with MCA course . here I am giving you information about required eligibility for Indian engineering service examination..

Educational Qualifications
You have to pass A degree in Engineering from a well recognized university or equivalent.

Or you have to pass M.Sc degree or its equivalent with Wireless Communications, Electronics, Radio Physics or Radio Engineering as special subjects for certain Services/posts only.

Age-limits
21-30 years on 1st August of the year of Examination.

Categories of which recruitment is made through the Examination
i. Civil Engineering
ii. Mechanical Engineering
iii. Electrical Engineering
iv. Electronics & Tele-communication Engineering