As far as I know there is no direct way to view GitHub issues in Jira. Probably one of the Apps might be of use. Just check them out - https://marketplace.atlassian.com/search?query=github.
Otherwise if you want to do it yourself then you can do it using the wonderful APIs provided by GitHub and Jira.
Another good things is that webhooks are available for Jira (Server and Cloud) and Github. Following links might help:
Whenever an issues changes you can push the changes to other side using hooks.
Good detailed answer. I did not find the appropriate plug-in in the https://marketplace.atlassian.com/search?query=github. If you will have found, please inform me. (I do not want to develop my app using API, so I want to use the existing solution).
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