B.A Sociology

Yes, definitely a candidate from any stream can study sociology. You can do graduation course after class 12th, which is a three year degree course.
After completing graduation, you can also do Master's degree in sociology and even research works also.
One can excel in this subject if he/she has real eagerness about this field which is all about reading and understanding human nature and behavior.

Hello Laxmi,
I have actually not understood. You were able to complete your BA based on 10th? If yes, then what's the need for doing 12th now? But if you have obtained degree from UGC approved university, then of course it remains valid.

Yes. Do you have any specific college to pursue your distance education?

For any degree course you will need to clear your 12th, so you should focus on the same.