Reservists Opportunity Act of 2021 This bill requires the Department of the Army to ensure that members of its reserve components may access the Tour of Duty system using a personal internet-enabled device. The Tour of Duty system is an online system of listings for opportunities to serve on active duty for members of the reserve components of the Army through which such members may apply for the listed opportunities. The Department of the Army may restrict access to the system on personal devices if the restriction is necessary for security reasons.