Is there any departmental exam to become officer from Sepoy in Indian Army?

Yes, they have ACC entry for that.

Hi Sanil, The first rank they start with is that of a sepoy or rifleman. After serving in that rank for around 5 years, a sepoy is promoted to Lance Naik(one arm strip). After another 4-5 years, he is promoted to Naik (corporal in western armies). A naik wears 2 arm strips. Now comes the next promo