Clinical Psychology

Hi.

Yes — internships are possible for BA Psychology students

Psychology internships allow undergraduates to “apply theoretical knowledge to real-life situations” — in clinics, hospitals, wellness centers, research labs, schools, community-service centres, NGOs, etc.

Some mental-health / wellness centers explicitly offer internship/trainee-positions to BA or BSc psychology students. For example, Peace of Mind (India) offers “graduate internship (BA/BSc Psychology or Clinical Psychology)” which includes patient-center workflow, admin support, content-creation, and “live-project” work.

Similarly, Inspiron Psychological Well‑Being Centre offers internship programs to students enrolled in bachelor or master psychology courses; they provide both online and offline internship/training options, including exposure to therapeutic approaches, case discussions, assessments, and counselling-skills training. 

On the “organisational/industrial-psychology” side, there are internship-type programmes focusing on employee behaviour, workplace psychology, HR, organisational development, etc. For example, Indian Counselling Services offers “Industrial and Organizational Psychology Internship” (with certificate/letter) aimed at those interested in organisational psychology.

See, earlier, the conventional path to apply for an RCI licensure was the MPhil, which has been phased out. So now, what you can do is to search for the institutes that are RCI-approved. They will provide the training and professional courses in fields related to rehabilitation and special education, for example, Clinical Psychology.
Some top RCI-approved institute options you'll find for a PhD in Clinical Psychology are:

• National Institute of Mental Health & Neuro Sciences (NIMHANS), Bengaluru
• Banaras Hindu University (BHU), Varanasi
• Central Institute of Psychiatry (CIP), Ranchi
• Jamia Millia Islamia University, New Delhi
• Tata Institute of Social Sciences (TISS), Mumbai
• Christ University, Bangalore
• Delhi University, New Delhi
• Amity University, Noida