In this work, we study the impact of the multiplicative phase noise in an IRS-assisted system. We consider an IRS-assisted system with multiplicative phase noise both at the BS and user. A novel channel estimation algorithm is proposed considering the phase noise. By utilizing the proposed channel estimates we investigate the system performance in the downlink, more specifically, we derive the ergodic capacity in closed form. Simulation results verify the correctness of the closed-form expression. We observe that the system becomes more robust against the phase noise as the number of reflective elements increases. Moreover, the influence of the additive channel noise in uplink vanishes as the number of reflecting elements grows asymptotically large.