This can be done with Automation for JIRA. Simply use the "Assign Issue" action and select "Assign to a member of a list or group". You will be then offered choice of "Load Balanced", "Round-robin" and "Random".
Load balanced assigning executes the given JQL and then looks for the users with lowest number of tickets assigned to them. This is great for Service Desks.
I have written this up in more details at:
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