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Driven or self-propelling particles moving in viscoelastic fluids recently emerged as a novel class of active systems showing a complex yet rich set of phenomena due to the non-Newtonian nature of the dispersing medium. Here we investigate the one-dimensional growth of clusters made of active colloidal shakers, which are realized by oscillating magnetic rotors dispersed within a viscoelastic fluid and at different concentrations of the dissolved polymer. These magnetic particles when actuated by an oscillating field display a flow profile similar to that of a shaker force dipole, i.e., without any net propulsion. We design a protocol to assemble clusters of colloidal shakers and induce their controlled expansion into elongated zigzag structures. We observe a power law growth of the mean chain length and use theoretical arguments to explain the measured 1/3 exponent. These arguments agree well with both experiments and particle based numerical simulations.