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".
Round-robin assigning iterates over a list of users and assigns issues to them in turn. I have written this up in more details at:
Hey Community mates! Claire here from the Software Product Marketing team. We all know software development changes rapidly, and it's often tough to keep up. But from our research, we've found the h...
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