Table partition in aws MYSQL RDS master slave setup
First, let's discuss what benefit you will get from partitioning.  Please provide SHOW CREATE TABLE (with the partitioning).  Partitioning, in itself, does not provide any performance benefits.  Let's see the query/queries that you think will benefit.

pt-online-schema-change is likely to be a way to convert to partitioning with virtually no downtime.  But check carefully; there may be restrictions on partitioning.

The manual says nothing about whether you can have replication between a non-partitioned on the master and a partitioned table on the slave.  The silence of the manual worries me; there could be issues.