Interest in plasma-liquid interaction phenomena has grown in recent years due to applications in plasma medicine, water purification, and plasma-hydrocarbon reforming. The plasma in contact with liquid is generated, for example, using the plasma jets or streamer discharges. The interaction between the streamer and water can cause both physical and chemical modifications of the liquid. In this paper, the interaction between an anode-directed streamer and the de-ionized water is studied using one-dimensional particle-in-cell Monte Carlo collisions model. In this model, plasma species in both gas and liquid phase are considered as the macro-particles. We find that the penetration of the streamer head into the liquid causes ionization of water molecules by electron impact, a process which is usually ignored in the fluid models. The main charge carriers in the liquid phase are negative water ions which agree with earlier experimental and computational modeling studies. Additionally, we observe an ion-rich sheath in the vicinity of the water surface on the gas side.