The eligibility criterion to do graduation in Psychology is only passed in 10+2 with minimum 45-50% marks depending on the university criteria in any stream- it could be science, commerce or humanities or students of International Board can also apply.
The criteria for selection in each university are different like some conduct an entrance test and then the interview where as in some universities there is only a merit base selection criterion. So you can see and apply accordingly.
So you need not worry and apply for it can study the same. Some of the good universities to study Psychology in are:
1. University of Delhi
2. Jamia Millia Islamia University
3. Punjab University
4. University of Calcutta
5. Kurukshetra University
You can fill the forms for the university you want to apply in.