Phase-locking (frequency entrainment) of an oscillator, in which a periodic extrinsic signal drives oscillations at a frequency different from the unperturbed frequency, is a useful property for study of oscillator stability and structure. The cell cycle is frequently described as a biochemical oscillator; however, because this oscillator is tied to key biological events such as DNA replication and segregation, and to cell growth (cell mass increase), it is unclear whether phase locking is possible for the cell cycle oscillator. We found that forced periodic expression of the Gi cyclin CLN2 phase locks the cell cycle of budding yeast over a range of extrinsic periods in an exponentially growing monolayer culture. We characterize the behavior of cells in a pedigree using a return map to determine the efficiency of entrainment to the externally controlled pulse. We quantify differences between mothers and daughters and how synchronization of an expanding population differs from synchronization of a single oscillator. Mothers only lock intermittently whereas daughters lock completely and in a different period range than mothers. We can explain quantitative features of phase locking in both cell types with an analytically solvable model based on cell size control and how mass is partitioned between mother and daughter cells. A key prediction of this model is that size control can occur not only in Gi, but also later in the cell cycle under the appropriate conditions; this prediction is confirmed in our experimental data. Our results provide quantitative insight into how cell size is integrated with the cell cycle oscillator.