Definitely you can do your PhD from abroad. If you have a desire to pursue research abroad then you must go because, there are lots of fellowship programs and fee waivers are available all over the world for international students as well as Indian students specifically. The first step is to search different PhD programs online through various websites like ‘Find_a_PhD.com’ etc. Then, once you select a particular program, see the Supervisor/Prof. handling that project and contact him through mail and show your interest by mentioning your qualifications and skills. In many PhD applications you need to apply directly to the institution so that’s a different case. But, now a days many PhD positions are based on the funded research projects. In that case, the project is sanctioned to a Professor working in that arae and then you will work under that professor in that project for your PhD. In this case, contacting professor directly and sending your CV would be beneficial for you to get selected there.
Nishant Kumar Sahu, former International Visiting Researcher at Industrial Technology Research Institute (2020)
Source: Quora Digest