Trajectory control of spatial solitons is an important subject in optical transmission field. Here we investigate the propagation dynamics of Laguerre-Gaussian soliton arrays in nonlinear media with a strong nonlocality and introduce two parameters, which we refer to as initial tangential velocity and displacement, to control the propagation path. The general analytical expression for the evolution of the soliton array is derived and the propagation properties, such as the intensity distribution, the propagation trajectory, the center distance, and the angular velocity are analyzed. It is found that the initial tangential velocity and displacement make the solitons sinusoidally oscillate in the x and y directions, and each constituent soliton undergoes elliptically or circularly spiral trajectory during propagation. A series of numerical examples is exhibited to graphically illustrate these typical propagation properties. Our results may provide a new perspective and stimulate further active investigations of multisoliton interaction and may be applied in optical communication and particle control.