Answer from Shekar Dattatri, Conservation India:
Despite not having a background in Biology or Zoology, you can have a career in wildlife conservation. The best way to start might be to join the Masters’s Degree in Wildlife and Conservation Biology offered by the National Centre for Biological Sciences (NCBS) in Bangalore. This is an extremely tough course to get into as seats are limited and the competition is fierce. However, if you succeed, you will get a solid foundation to start a new career in this direction.
You can also apply to organizations like Wildlife Trust of India, Wildlife Conservation Society (India Program) or Wildlife SOS and see if they have a job opening for someone with your skills.