According to me yes after completing BTECH you can apply for UPSC Indian Engineering Services exams and here I will let you know information about the exam.

The recruitment of qualified candidates is made under the following categories:
Electronics & Telecommunication Engineering
Electrical Engineering
Mechanical Engineering
Civil Engineering

Eligibility
Age:-
Aspirants aged between minimum 21 and maximum 30 years.

Educational Qualification:-
B.E./B.Tech or passed sections A and B of the Institution Examinations of the Institution of Engineers (India) or

Obtained a degree/diploma in engineering from such foreign university/college/institution recognized by the Government of India from time to time.

Passed Graduate Membership Examination of the Institute of Electronics and Telecommunication Engineers (India); or

Passed Associate Membership Examination Parts II and III/Sections A and B of the Aeronautical Society of India; or

Passed Graduate Membership Examination of the Institution of Electronics and Radio Engineers, London held after November, 1959.

Nationality:-
The aspirant must be any one of the following:
A citizen of India
A citizen of Nepal or a subject of Bhutan
a person of Indian origin who has migrated from Pakistan, Myanmar, Sri Lanka, Kenya, Uganda, Tanzania, Zambia, Malawi, Zaire, Ethiopia or Vietnam with the intention of permanently settling in India.

Departments Allocation Through ESE
A. Electronics Engineering
Indian Railway Service of Signal Engineers
Indian Railway Stores Service
Indian Telecom Service Group-A
Central Power Engineering Service (E&T Posts)
Engineer GCS Group A in WPC/MO(M/O Communication & IT)
Indian Inspection Service Group A (E&T Posts)
Indian Supply Service Group A (E&T Posts)
Indian Ordnance Factories Services
Assistant Naval Store Officer Grade-I in Indian Navy
Indian Naval Armament Service
Assistant Executive Engineer in Corps of EME, Ministry of Defence

B. Electrical Engineering
Indian Railway Service of Electrical Engineers
Indian Railway Stores Service
Indian Defence Service of Engineers(Electrical Posts)
Central Mechanical & Electrical Engineering Service (Electrical Post)
Central Power Engineering Service (Electrical Post)
Indian Ordnance Factories Services
Indian Supply Service Group A (Electrical Posts)
Assistant Naval Store Officer Grade-I in Indian Navy
Indian Naval Armament Service
Assistant Executive Engineer in Corps of EME, Ministry of Defence

C. Mechanical Engineering
Indian Railway Service of Mechanical Engineers
Indian Railway Stores Service
Indian Defence Service of Engineers
Central Mechanical & Electrical Engineering Service (Mechanical Post)
Central Water Engineering Service Group-A (Mechanical Post)
Central Power Engineering Service (Mechanical Post)
Indian Ordnance Factories Services
Indian Inspection Service Group A
Central Engineering Service (Roads) Group-A
Indian Supply Service Group A (Mechanical Posts)
Assistant Executive Engineer Group A Geological Survey of India
Assistant Naval Store Officer Grade-I in Indian Navy
Indian Naval Armament Service
Assistant Executive Engineer in Corps of EME, Ministry of Defence

D. Civil Engineering
Indian Railway Service of Engineers
Central Engineering Service
Indian Defence Service of Engineers
Indian Railway Stores Service
Central Engineering Service (Roads) Group-A
Central Water Engineering Service
Indian Ordnance Factories Services
AEE in P&T building works Group-A Services
AEE in Border Road Engg. Services GR-A