Atlassian JIRA does not support OpenJDK. Oracle has changed it licensing for Oracle JDK. With that in mind, the goal is to use OpenJDK as a replacement for the Oracle JDK. This is possible and easy to do.
Search for your jira install %JIRA_HOME/jira/bin/check-java.sh. On the line that contains "java version" change it to "openjdk version", then restart your install of JIRA.
sed -i 's/java version/openjdk version/g' check-java.sh -i.bak
If you don't already have OpenJDK installed and are using CentOS 7. The install is easy enough too.
yum install java-1.8.0-openjdk-devel
You should see something similar to this for a successful implementation of OpenJDK with JIRA.