A nanoscale conduit that preferentially transports a selected charge provides a unique opportunity of studying charge-specific chemistry in 1D space, single-molecule transport and detection, and novel charge storage devices. The π-electron-rich surface of single walled carbon nanotube (SWNT), being theoretically predicted to strongly interact with cations, potentially allows charge-specific transport of ions. Here we demonstrate via surface analyses the first experimental evidence of cation-selective ionic transport along the exterior of SWNTs under electric field, while anions slowly counter-diffuse along the substrate adjacent to the nanotubes. The counter-flow of spatially separated charges at different fluxes causes ionomigration of water molecules toward cathode, thereby pumping micro-droplets of electrolytes along the nanotubes near anode, followed by their sequential migration toward cathode. The micro-droplets containing hygroscopic NaCl not only help optically visualize individual nanotubes for an extended period of time, but serve as micro-lenses that enhance Raman scattering of nanotubes by up to two orders of magnitude. Our study on the relatively-overlooked exterior of SWNTs presents how the cation-π interaction leads to spatiotemporal non-uniformity during transport of ions, a 1D analog of ionomigration observed in biological systems and bulk ionic crystals.