Can I join LLB after completing BA in Political Science Hons. in Asian Law College?

Yes, you can join but you need to have atleast 45% - 55% to enroll in the Bachelor's degree in law.

If you wish to apply to Asian Law College for LLB then you are eligible as you need to have graduated from a recognised college/ university with a minimum of 45% marks (40% for SC/ ST/ OBC candidates). You need to also qualify the Asian Law College Admission Test.