Optical nanofibers have recently emerged as attractive nanophotonic platforms for many applications ranging from quantum technologies to nonlinear optics, due to both their tight optical confinement and their wide evanescent field. Herein we examine theoretically the optical Kerr effect induced by the evanescent field of a silica nanofiber surrounded by different nonlinear liquids such as water, ethanol and acetone and we further compare them with air cladding. Our results show that the evanescent Kerr effect significantly dominates the usual Kerr effect inside the silica core for sub-wavelength diameters below 560 nm, using acetone. We further report the observation of the evanescent Kerr effect through surrogate measurements of stimulated Raman-Kerr scattering (SRKS) in an acetone-immersed silica nanofiber. Our findings open the way towards potential applications of optical nanofibers to ultra-sensitive liquid sensing or to enhancing the nonlinear effects through the evanescent field.