Hi, yes being from a science background you can become a Psychologist. After completing your +2 you can apply for graduation in either BA Psychology or BSc Psychology. Most of the colleges require you to pass 10+2 with a minimum 50% marks in aggregate preferably with Psychology as one of the subjects. After completing your graduation you can apply for MA/ MSc in psychology and then start working or further continue your studies. In order to get licensed to practice Psychology you need a degree in psychology and you will have to pass a state and/or national exam and fulfill other licensing requirements.
You shouldn't have to face any major difficulties in applying for graduation course in psychology as long as you meet the cutoff percentage. And the first year syllabus covers everything that one would have studied in 11th and 12th if they had Psychology as one of the subjects.
Being from science stream you can apply for both ba abd bsc in psychology as meeting the stream requirement of particular colleges is also important. Most colleges offer BA to those from arts stream or those who had Psychology as one of the subjects in +2. But if that's not the case with you you can try and apply for both courses.
Some top colleges in India for Psychology are:

• LSR college, new Delhi
  
• Jesus and Mary's college,new Delhi
  
• Gargi college, New Delhi
  
• Jamia milia islamia, New Delhi
  
• Christ University, Bangalore
  
• Fergusson college, Pune
  
• Symbiosis international University, Pune
  
• Mount Carmel college, Bengaluru
  
• Banaras Hindu University, Varanasi
  

• Good luck