The formation and subsequent self-organization of a spiral electron density modulation initialized in a plasma produced by optical-field ionization of various gas species is studied. Our analytical model predicts that the spiral density modulation results from space-dependent drift velocities of the ionized electrons due to the spatial and temporal intensity distributions of the circularly polarized ionizing laser. The spiral topology of the electron density has been validated by three-dimensional particle-in-cell simulations. Simulations further show that the spiral density modulation subsequently self-organizes to form numerous microfilaments, i.e., thin strands that arise because of a modified streaming instability.