Surface wrinkles are commonly observed in soft polymer nanofibers produced in electrospinning. This paper studies the conditions of circumferential wrinkling in polymer nanofibers under axial stretching. A nonlinear continuum mechanics model is formulated to take into account the combined effects of surface energy and nonlinear elasticity of the nanofibers on wrinkling initiation, in which the soft nanofibers are treated as incompressible, isotropically hyperelastic neo-Hookean solid. The critical condition to trigger circumferential wrinkling is determined and its dependencies upon the surface energy, mechanical properties, and geometries of the nanofibers are examined. In the limiting case of spontaneous circumferential wrinkling, the theoretical minimum radius of soft nanofibers producible in electrospinning is determined, which is related closely to the intrinsic length l_{0}=γ/E of the polymer (γ: the surface energy; E: a measure of the elastic modulus), and compared with that of spontaneous longitudinal wrinkling in polymer nanofibers. The present study provides a rational understanding of surface wrinkling in polymer nanofibers and a technical approach for actively tuning the surface morphologies of polymer nanofibers for applications, e.g., high-grade filtration, oil-water separation, tissue scaffolding, etc.