It is known that the turbulence in a fast-rotating volume becomes effectively two-dimensional. The latter is characterized by an inverse energy cascade leading to the formation of coherent flow in finite systems. In a rotating three-dimensional vessel this flow has the form of columnar vortices. Here we develop an analytical theory describing interaction of the vortex with turbulent pulsations. This interaction results in energy transfer from small-scale eddies to the large-scale vortex. We derive the equation for the radial velocity profile of the vortex and solve it for the simplest boundary conditions. We indicate the domain of physical parameters where our theory works.