Hey Pratyush.

A student from Science stream is very much eligible to pursue law after 12th. There are various entrance examinations for admission in 5 year integrated law course like BA LLb, BBA LLb etc. Admission is based on your  scores and rank in the entrances. You will have to fill the forms for the entrances you want to take. Last day for many is in February end/ March.

 CLAT- All National Law Universities

AILET- National Law University Delhi

SLAT- Symbiosis Law School

LSAT- All Private Law colleges

IPU CET- IP University

PU BA/BCOM LLb- Panjab University, Chandigarh 

MHCET- GLC Mumbai, ILS Pune, and other law colleges in Maharashtra 

Christ University 

TS LAWCET Etc

Best of luck.