The paper aims to study the response of a solar small-scale and weak magnetic flux tube to photospheric twisting motions. We numerically solve three-dimensional ideal magnetohydrodynamic equations to describe the evolution of the perturbation within the initially static flux tube, excited by twists in the azimuthal component of the velocity. These twists produce rotation of the magnetic field lines. Perturbation of magnetic field lines propagates upwardly, driving vertical and azimuthal flow as well as plasma compressions and rarefactions in the form of eddies. We conclude that these eddies result from the sheared azimuthal flow which seeds Kelvin-Helmholtz instability (KHI) between the flux tube and the ambient medium. Numerically obtained properties of the KHI confirm the analytical predictions for the occurrence of the instability.