Yes, You can. Scope is wide. Automobile Engineers are demanded in both India and abroad. As its a huge industry, there are great employment opportunities in Private National and Multinational Automobile companies, Service Stations, Private Transport companies, Defense Services and Self Employment by setting up Automobile Garage or Maintenance Workshop.

Automobile Engineering has gained recognition and importance ever since motor vehicles capable for transporting passengers has been in vogue. Now due to the rapid growth of auto component manufacturers and automobile industries, there is a great demand for Automobile Engineers. Automobile Engineering alias Automotive Engineering or Vehicle Engineering is one of the most challenging careers in the field of engineering with a wide scope.
As Design Engineers, automobile engineers design the intricate details of the hydraulic, electrical, and mechanical systems inside a vehicle.
As Development Engineers, they are involved in the development, implementation, operation, maintenance, and control of all processes in the manufacture of vehicles.
As quality control executive, they work towards improving the efficiency of existing vehicles and developing new ones.
Along with this, graduates and postgraduates may fetch following jobs in the automobile industry:
Automobile Engineer
Material Processing Specialist
Safety Testing Specialist
Material Purchase Manager
Quality Control Executive
Research and Development Engineer
Automobile Technicians
Automobile Designers
Bike Mechanics
Car Mechanics
Mechanical Design Engineer
Quality Engineer
Diesel Mechanics
Executive and Managerial Positions
Senior Production Engineer
Driver Instrumentation Engineer
College offering this course are:
IIT Bombay, ICT Mumbai ,IIT- Delhi, IIT- Hydrabad, IIT -Roorkee , DTU Anna University

Yes definitely. Great scope in automobile in india.
Introduction - Automobile Engineering is a branch of engineering that deals with designing, manufacturing and operating automobiles. It incorporate elements of mechanical, electrical, software and safety engineer as applied to design and manufacture buses, bikes, trucks and other vehicles and machines.
  The course in Automobile Engineering deals with the creation and maintenance of automobiles, starting from designing the vehicles to manufacturing components, assembling and testing them for safety.

Persuing -
Basic Eligibility for UG courses-
The students, who wish to pursue automobile engineering, should have qualified Class 12thwith minimum 50% marks in Physics, Chemistry and Mathematics from a recognized board in India. Candidates, who wish to join IITs, should have cleared JEE Main and Advanced. Whereas, admission to NITs depend on candidates JEE Main score.

Automobile Engineering Course -

Few courses in this field are:
Diploma in Automotive Engineering,
Bachelor of Engineering in Automotive Engineering, Bachelor of Technology in Automotive Engineering,
Master of Technology in Automotive Engineering,
Master of Technology in Automotive Engineering,

Top colleges for studying Automobile Engineering (under Mechanical Engineering branch) -
IIT Bombay, IIT Delhi, IIT Kharagpur, IIT KANPUR, IIT Mandi, IIT Madras, IIT Bhubaneswar, IIT Hyderabad, IIT ROORKEE, IIT Indore, NIT Tiruchirappalli, NIT Warangal, NIT Karnataka,NIT  Surathkal, NIT Calicut, NIT Hamirpur, NIT Delhi, Maulana Azad National Institute of Technology BHOPAL, Motilal Nehru National Institute of Technology Allahabad, Malaviya National Institute of Technology JaipurVisvesvaraya, National Institute of Technology, Nagpur, BITS PILANI, VIT University, SRM University, Manipal University..

AUTOMOBILE ENGINEERING  GROWTH, SCOPE & Opportunities -
One of the fastest growing industries, India is the 7thlargest producer in the world with an average annual production of 17.5 million vehicles. This sector contributes 7% of the countrys GDP by volume. According to a report of Society of Indian Automobile Manufacturer (SIAM) 2015, our country is also the 4thlargest automotive market by mass.

According to industry estimates, automobile sector is expected to sell more than 6 million vehicles by 2020. The latest report by SIAM also says that in April-March 2015, overall automobile exports grew by 14.89% over the same period last year.
Looking at this data, it is clear that India is a potential engineering automobile market and jobs in this sector is expected to grow significantly.
Salary Range-
The salary package of an engineer depends on many factors like size of the organization, profile, qualification, experience and company location. It also depends on your institute from where you have completed your engineering. Typically, students from IITs or NITs earn more than those graduated from a private college(around 15k-20k for beginners)