A step stress deforming suspended cells causes a passive relaxation, due to a transiently cross-linked isotropic actin cortex underlying the cellular membrane. The fluid-to-solid transition occurs at a relaxation time coinciding with unbinding times of actin cross-linking proteins. Elastic contributions from slowly relaxing entangled filaments are negligible. The symmetric geometry of suspended cells ensures minimal statistical variability in their viscoelastic properties in contrast with adherent cells and thus is defining for different cell types. Mechanical stimuli on time scales of minutes trigger active structural responses.