Hii!
The eligibility criteria for pursuing Bachelor's degree in psychology, states that the candidate must have passed class 12th with minimum 50% marks in any subject stream with English as compulsory subject form a recognised Board of education.
So, Yes. You can pursue psychology after class 12th without any problem.
Talking about the entrance criteria, most of the Colleges conduct entrance exams for admissions. Class 12th syllabus is asked, basically. So, study well.
Hope this helps.
Good luck!