This is a bit of a mixed answer but let me give it a go. The short answer in - not OOTB in the way you have stated.
For Classic projects not OOTB yet. Now with the recent intro of Advanced roadmaps there is a view of progress for Epics though it is not exactly percentage unless every child story happens to be equal as it displays number of stories complete vs incomplete. Finally this is only currently in Premium Jira. They are adding roadmaps to Classic soon but unsure if it will have this feature or not.
For NG projects there is also a view of progress under Roadmaps.
i would recommend looking at addons. There is one I have previously used called Epic Sum Up that was pretty good at giving a view of progress as I recall.
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