Yes you can definitely get into IIMs. With an excellent academic records you are a non engineer which gives you an extra edge over other students.

For getting admission in IIMs first of all.you need to prepare very well for CAT exam and score a very high percentile. Higher the percentile higher will be your chance of getting a call from top IIMs.

After CAT exam every IIM makes a merit list to call students for next round of interview and WSAT which is based on your aggregate score which comprises of many factors such as CAT marks, 10th 12th and graduation percentage, work experience, engineer or non engineer, gender with different weightages for different colleges. Being a non engineering you will get extra 3% marks in your aggregate score.

To get calls from top 3 IIMs like IIM A, B and C you need to score atleast above 99 percentile. For other old IIMs like IIM L, K and I you need to score above 97 percentile. With 93+ percentile you can get calls from all new IIMs. This is all a tentative percentile on the basis of last few years records. As I mentioned above CAT marks is not the only criteria so getting a call depends on your overall profile.

After you get a call then you need to through a second round of interview and WSAT. After this a final merit list is made including marks of interview and WSAT which generally has highest weightage in final list along with CAT marks. This merit list is used to call students for admission.

So your first basic step is to prepare for CAT exam. All the best for your preparations!!