Mechanical agitation is typically used to fragment and disperse insoluble materials in a solvent. We report here an aggregation process that, contrary to expectation, is induced by mechanical agitation: when aqueous dispersions of single-walled carbon nanotubes (SWNTs) are subject to vortex-shaking, weakly bound micron-sized aggregates are formed. The SWNT dispersions are prepared by adding various dispersants employing a sonication followed by centrifugation approach. While surfactant adsorption to the SWNTs during sonication results in stabilized exfoliated tubes and thin bundles, we find that vortex-shaking the fresh dispersions for short periods (10-60 s) results in re-aggregation into flocs in the 1-102 µm range. The aggregation is reversible: if the vortexed dispersions are mildly sonicated, the flocs break down and re-dispersal occurs. Imaging at different resolutions shows that the aggregates consist of loose networks of intertwined tubes and bundles. The data further indicate that the average aggregate size increases logarithmically with vortex time and is critically influenced by dispersant type (ionic or nonionic), centrifugation time (prior to vortexing) and initial concentration of dispersed SWNTs. These results are relevant if stabilization or destabilization of dispersions is sought for, i.e., in drug delivery or sensing applications, and could also be of interest for chiral sorting of SWNTs and percolation conductivity.