You can login to your RBL credit card net banking account at the official website of the bank. You can update your new number by feeding the required details. 

Visiting the branch: You can visit the nearby RBL branch and fill up a form requesting for a change of your contact details. 

You can download the change request form from the bank’s official website, fill up and send it to the address mentioned in the form or submit at the nearby RBL branch. 

Also, you can call up the customer care to get information on how to change your RBL bank credit card