Hey.
Yes,  you can study law after you've completed graduation in any field. After BBA you can go for a 3 year Law degree. Admission to most colleges is through entrances. Eligibity criteria requires you to score a minimum aggregate of atleast 45-55% marks in graduation degree according to the entrance/ institute.

Here is a list of law entrances for 3 year LLB course

- DU LLB - Delhi University

MH CET- GLC mumbai, ILS Pune and other colleges in Maharashtra

SLAT- Symbiosis Law school

PU LLB- Panjab University, Chandigarh 

LSAT- Jindal global Law school, IIT Kharagpur and other private law colleges

BHU LLB- Banaras Hindu University

BVP LLB- Bharatiya Vidyapeeth

TS LAWCET Etc

Best of luck!

 Ofcourse yes!! You can join 3 years LLB course in some good college like DU, BHU or even other colleges.