Hi Ritu,

Yes, you have to give the GMAT exam or GRE ( depending on your subject) so as to apply for the PhD programs. It is a prerequisite in almost all major universities. Alongwith the score you need to submit a SOP, Documents, recommendation letters and research proposal. 

Do you have in particular University in mind? The application cycle for Phd opens in August- sept and results come out by March. You can check in the university's website for the exact application date. As you know, PhDs are mostly funded and so can be highly competitive. Make sure you have a good score, research proposal with you. Researching the faculty of your chosen university would also help ; alternatively you can also contact them and figure out if you want to work with a chosen supervisor. Choosing a good supervisor is important because you will be working with this person for quite a few years but most importantly, be 100% sure of your research interests. During the program, you will also be given TA/RA opportunities ( teaching or research assistant) so make the most of the opportunity if you really want a career in academia.

Feel free to ask if you have any more queries.

good luck!