Atmospheric turbulence causes beam broadening and beam wander in vortex beams during propagation. Based on the Rytov perturbation theory, the Huygens–Fresnel principle, and the beam wander theory, analytical expressions for the beam width and variance of beam wander of vortex beams propagating through atmospheric turbulence are derived. The effects of propagation distance, turbulence intensity, and topological charge on beam width and beam wander are discussed. Field experiments verify the influence of topological charge on beam broadening and beam wander trends. The results mainly include the following: (1) The beam width of vortex beams is larger than that of Gaussian beams, while the variance of beam wander is smaller. (2) As the topological charge increases, the beam width increases while the variance of beam wander decreases. (3) Longer wavelengths and larger initial beam waists lead to increased beam width but decreased variance of beam wander. (4) Stronger turbulence intensity results in increased beam width and variance of beam wander. This study provides both theoretical and experimental foundations for vortex beam propagation in random media, thereby improving the theoretical framework for vortex beam transmission through atmospheric turbulence.