The actual state of cross compiling rethinkdb for raspberry-pi is complicated right now. It seems that this is not actively maintained and it became complicated to set it up over the years. This is however possible with a little bit of effort. It requires dwelving into the rethinkdb build framework based on good ol' makefiles...
You can find an attempt at doing so here in a Dockerfile. It basically creates a Docker container with all the dependencies (especially the cross compiler), modify the config and build rethinkdb. The outcome is the rethinkdb package for raspberry.
You can either use it as is or have a look to it and reproduce it on your own.