This work addresses the problem of learning from large collections of data with privacy guarantees. The sketched learning framework proposes to deal with the large scale of datasets by compressing them into a single vector of generalized random moments, from which the learning task is then performed. We modify the standard sketching mechanism to provide differential privacy, using addition of Laplacenoise combined with a subsampling mechanism (each moment iscomputed from a subset of the dataset). The data can be divided be-tween several sensors, each applying the privacy-preserving mech-anism locally, yielding a differentially-private sketch of the whole dataset when reunited. We apply this framework to thek-meansclustering problem, for which a measure of utility of the mechanism in terms of a signal-to-noise ratio is provided, and discuss the ob-tained privacy-utility tradeoff.