The cross section of the process $e^+e^- to K^+K^-$ was measured in the energy range $sqrt{s}$ = 1.04--1.38 GeV in the SND experiment at the VEPP-2M $e^+e^-$ collider. The measured cross section is described by the model of vector meson dominance with contributions from the light vector mesons $rho$, $omega$, $phi$ and their lowest excitations. The mean statistical accuracy of the measurement is 4.4 %, and the systematic uncertainty is 5.2 %.