The ice will float with a fraction of the ice cube sticking above the surface which is determined by the ratio of the density of water to the density of ice. Since these densities do not change as the ice melts, the fraction of ice above the water surface will never change. Since the fraction of ice above the water's surface never changes, the volume decrease of ice below the water surface during melting is always exactly replaced with an equivalent volume of melt. Therefore the water level in the glass will not change throughout the melting process.