Yes, BHU does offer BSC and BA programme in psychology. It is a renowned course of BHU.

There are many other colleges which offer the same programme.

Delhi University

Jamia Milia Islamia(New Delhi)

Ambedkar University (New Delhii)

Panjabi University (Chandigarh)

Aligarh Muslim University

And of course Banras Hindu University (Varanasi)

All the best