A refrigerator appliance having a dispensing system and a method for dispensing liquid into a container are provided. The dispensing system can be an autofill dispensing system. In one example aspect, the dispensing system includes a vibration generator and a measurement device. When a container is present in a preselected position, liquid is delivered to the container. As liquid fills into the container, the vibration generator propagates vibrations through the container. The measurement device detects one or more characteristics of the vibration and routes one more signals indicative of the characteristics to a controller of the system. The controller determines a liquid fill level of liquid within the container based at least in part on the signals received from the measurement device.