Elastic search node replication

Can we configure elasticsearch replication to act as PRODUCTION and DR in different data centers?

No. Not really nowadays.

You can still run periodical Snapshots in the PROD DC and then sync the files to the DR DC.
If you want to maintain that in real time, then you have to index in both DC at the same time.

Can you please let me know how can we do indexing on both DC's ?

From your application, send the data twice basically.

Or use a message broker and read it with logstash from both DC.

That's what I'd do.