A clear ice making system and method utilizes an ice tray including a plurality of ice forming cavities extending into a fluid supply cavity. Fluid supplied to the fluid supply cavity flows into each of the plurality of ice forming cavities and out through respective fluid outlets located in a bottom portion of the ice forming cavities to a fluid outlet chamber below. Cooled ice forming members extend into respective ice forming cavities. Fluid is continuously cycled through the ice forming cavities and around the ice forming members during an ice making event such that clear ice pieces gradually form on each of the ice forming members. During an ice harvest event, ice forming members are heated to release formed ice pieces, and the ice pieces are transferred from a fresh food compartment of a refrigerator to an ice storage bucket located in a freezer compartment of the refrigerator.