I cannot answer for sure, but AFAIK, there is no Marriott branded credit card outside the US.

The websites of the Courtyard Chennai & JW Marriott Hotel Mumbai both have a link to the Marriott Rewards Visa. However, when clicking on the link, the fine print says "You must have a valid permanent home address within the 50 United States or the District of Columbia."

There are other travel rewards cards. I know Standard Chartered offers some, but not Marriott specific.