Is it possible to deploy RDS in multiple region in AWS with read and write replica
You can look at Aurora Global Database for this. Based on this news announcement, you can also configure the setup, so you can write to your local db cluster and this is forwarded to your primary region.
Of course there would be some lag in write requests, essentially of the length of time it takes to write to the primary region and replicate the data changes back to the replica in your local region. Nonetheless this is likely easier to handle (and with the same methods in a web application), as if you wrote to the primary region yourself and checked if the data had arrived back in local replica.