The structure of Langmuir plasma waves carrying a finite orbital angular momentum is revised in the paraxial approximation. It is shown that the kinetic effects related to higher-order momenta of the electron distribution function lead to coupling of Laguerre-Gaussian modes and result in a modification of the wave dispersion and damping. The theoretical analysis is compared to the three-dimensional particle-in-cell numerical simulations for a mode with orbital momentum . It is demonstrated that propagation of such a plasma wave is accompanied with generation of quasistatic axial and azimuthal magnetic fields which result from the orbital and longitudinal momenta transported with the wave, respectively.