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Redshift-space distortions in the clustering of galaxy clusters provide a novel probe to test the gravity theory on cosmological scales. The aim of this work is to derive new constraints on the linear growth rate of cosmic structures from the redshift-space two-point correlation function of galaxy clusters. We construct a large spectroscopic catalogue of optically-selected clusters from the Sloan Digital Sky Survey. The selected sample consists of $43,743$ clusters in the redshift range $0.1<z<0.42$, with masses estimated from weak-lensing calibrated scaling relations. We measure the transverse and radial wedges of the two-point correlation function of the selected clusters. Modelling the redshift-space clustering anisotropies, we provide the first constraints on the linear growth rate from cluster clustering. The cluster masses are used to set a prior on the linear bias of the sample. This represents the main advantage in using galaxy clusters as cosmic probes, instead of galaxies. Assuming a standard cosmological model consistent with the latest cosmic microwave background constraints, we do not find any evidence of deviations from General Relativity. Specifically, we get the value of the growth rate times the matter power spectrum normalisation parameter $fσ_{8}=0.44\pm0.05$, at an effective redshift $z=0.275$.