A clear ice making system and method utilizes an ice forming tray pivotally connected to opposing side walls of an icemaker housing. Ice forming fingers of a dedicated evaporator extend into fluid within the ice forming tray, and are cooled by communication with the refrigerant circulating system of the refrigerator. A motor oscillates the ice forming tray about a longitudinal axis at a frequency of about 0.4-0.6 hertz as fluid channels freezes on the ice forming fingers over time, forming clear ice pieces. During an ice dispensing event, the motor pivots the ice making tray about the longitudinal axis such that fluid remaining within the ice making tray drains into a fluid reservoir below. The ice forming fingers are then heated to release the clear ice pieces for transfer from the fresh food compartment to the freezer compartment of the refrigerator.