Rally does have connector to JIRA and it uses REST. Get JIRA OnDemand trial (https://www.atlassian.com/software/jira/try/) and use this instruction (https://prod.help.rallydev.com/jira-5-installation-user-guide).
Depends on what you mean by "use with"? You can interact with OnDemand via REST if Rally has any capability to do that. The last time I looked, there was a Rally connector that uses SOAP, but that's deprecated, so I don't know if it will work with Jira 6.
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