Radar data have already proven to be compressible with no significant losses for most of the applications in which it is used. In the framework of information theory, the compressibility of a signal implies that it can be decomposed onto a reduced set of basic elements. Since the same quantity of information is carried by the original signal and its decomposition, it can be deduced that a certain degree of redundancy exists in the explicit representation. According to the theory of compressive sensing (CS), due to this redundancy, it is possible to infer an accurate representation of an unknown compressible signal through a highly incomplete set of measurements. Based on this assumption, this paper proposes a novel method for the focusing of raw data in the framework of radar imaging. The technique presented is introduced as an alternative option to the traditional matched filtering, and it suggests that the new modes of acquisition of data are more efficient in orbital configurations. In this paper, this method is first tested on 1-D simulated signals, and results are discussed. An experiment with synthetic aperture radar (SAR) raw data is also described. Its purpose is to show the potential of CS applied to SAR systems. In particular, we show that an image can be reconstructed, without the loss of resolution, after dropping a large percentage of the received pulses, which would allow the implementation of wide-swath modes without reducing the azimuth resolution.