Hello,
Yes you can join BA colleges based on class XII marks.
It will be difficult to get government colleges with these marks as cutoffs are usually higher for government colleges.
However you can get paid management seats in private colleges.
Fees would be high but you will definitely get a seat.
Contact the private college you are interested in directly for these seats.
Or you can go for universities/colleges which conduct entrance exams for admission to BA courses.

Good luck