Yes. You can invite someone to Zinc if you are not an admin by clicking the add person icon in the top right corner of the Recent screen of your mobile app.
This button will bring you to a Find Coworkers screen, where you can type in a specific person’s email address to the search box and send them an email containing a Zinc invitation.
This will NOT add them to your organization, it will only invite them to begin using Zinc. Adding members to an organization is reserved for certain types of admins (learn more about Admins and Admin Tiers here).