This paper is concerned with the consensus tracking problem for a class of nonlinear discrete-time multi-agent systems (MASs). The dynamic linearization method is used to approximate the nonlinear dynamics of the addressed MASs, resulting in an equivalent linear time-varying data model. With the purpose of mitigating the effects from limited communication bandwidth, a uniform-quantization-based encoding-decoding mechanism is exploited. A model-free adaptive distributed control protocol is put forward to deal with the tracking problem, which is totally data-driven without any requirement of model information except for I/O data. Finally, two illustrative simulation examples are utilized to demonstrate the effectiveness of the proposed control scheme.