For Ubuntu, oracle-java (7/8) installed. It'll be at this location /usr/lib/jvm and sudo access is required.
Create the file /etc/ld.so.conf.d/java.conf with the following entries:
/usr/lib/jvm/java-8-oracle/jre/lib/amd64
/usr/lib/jvm/java-8-oracle/jre/lib/amd64/server
(Replace java-8-oracle with java-7-oracle or java-7-openjdk-amd64 depending on your java version)
Then:
sudo ldconfig
Restart RStudio and then install the rJava package.