If you wish to give an Improvement examination then you can obviously do that while studying in your college, provided you should qualify at least the eligibility conditions required in your 10+2 result so that you can get admission in a college.

Also you must be aware if your board offers an Improvement examination or not. In some boards, a student can only reappear if he/she fails. So be sure that as well.

I hope this answer provides you some insight. Wish you a great day!