We study an intriguing new type of self-assembled active colloidal polymer system in 3D. It is obtained from a suspension of Janus particles in an electric field that induces parallel dipoles in the particles as well as self-propulsion in the plane perpendicular to the field. At low volume fractions, in experiment, the particles self-assemble into 3D columns that are self-propelled in 2D. Explicit numerical simulations combining dipolar interactions and active self-propulsion find an activity dependent transition to a string phase by increasing dipole strength. We classify the collective dynamics of strings as a function of rotational and translational diffusion. Using an anisotropic version of the Rouse model of polymers with active driving, we analytically compute the strings’ collective dynamics and center of mass motion, which matches simulations and is consistent with experimental data. We also discover long range correlations of the fluctuations along the string contour that grow with the active persistence time, a purely active effect that disappears in the thermal limit.