In this work, we exploit the radar clutter (i.e., the ensemble of echoes generated by the terrain and/or the surrounding objects in response to the signal emitted by a radar transmitter) as a carrier signal to enable an ambient backscatter communication from a source (tag) to a destination (reader). The proposed idea relies on the fact that, since the radar excitation is periodic, the radar clutter is itself periodic over time scales shorter than the coherence time of the environment. Upon deriving a convenient signal model, we propose two encoding/decoding schemes that do not require any coordination with the radar transmitter or knowledge of the radar waveform. Different tradeoffs in terms of transmission rate and error probability can be obtained upon changing the control signal driving the tag switch or the adopted encoding rule; also, multiple tags can be accommodated with either a sourced or an unsourced multiple access strategy. Some illustrative examples are provided.