Yes , you can get join in Indian navy as nurse after completing Bsc Nursing program . to join Indian nAy as nurse you have to appears and qualify the Military Nursing Service(MNS) exam.

Military Nursing Service(MNS) exam:
Eligibility :
Nationality –
Must be a citizen of India .

Qualification :
BSc (Nursing)/Post Certificate B.Sc (Nursing) in first attempt or
M Sc (Nursing).

Age Limit:
21 years -35 years of age .

Marital status :
Unmarried/Married/Divorcee/Widow

Medical Standards:
Applicants must be medically fit.

Physical standards:
Minimum Height –
148 cm

Minimum Weight –
39 Kgs

Method of Selection:
Written test
Medical test
Interview

Written Test Pattern :
90 minutes duration

Questions form :
General English,
Biology,
Physics,
Chemistry
General Intelligence.