Yes. Although usually the form of a copyright notice would be:
COPYRIGHT © AUTHOR YEAROFPUBLICATION
Under Section 55(1) and (2) of the Copyright Act of 1957, you must give the notice to receive any protection other than the right to seek an injunction ordering the infringer to cease using the work, and the notice creates a presumption that the statements in the notice regarding authorship are correct which must be overcome by an alleged infringer.
But, even though you are allowed to give that notice without registering the copyright with authorities in India, there are rights related to a copyright that you can secure only by registering the copyright in India under the Copyright Act of 1957, as amended, which is currently in force.
Some of the benefits of registration of a copyright in India are set forth at Section 48 of the Copyright Act of 1957, which provides that the registration of a copyright constitutes presumptive proof of all information contained in the copyright application including the date and authorship of the work, its non-infringement of any valid trademarks, its content, and its status as a copyrighted work. It also puts everyone on constructive notice of the existence of the registrant's rights. Registration will often reduce the amount of litigation costs and uncertainty for someone enforcing a copyright considerably, although unlike U.S. copyright litigation process, registration does not appear to be an absolute prerequisite for bringing an infringement lawsuit in India.
Registration also appears to be required to obtain the proceeds of a statutory license to use a copyrighted work when an individually agreed licensing agreement is not required (e.g. when someone does a cover version of a copyrighted song).