This paper addresses the issue of efficient crop irrigation from the perspective of precision agriculture, motivated by the fact that agriculture is responsible for 70 percent of fresh water extractions at a global level. In this paper we develop a methodology to design trajectories for efficient crop irrigation with Unmanned Aerial Vehicles (UAVs). The main goal is to supply sufficient water to avoid crop water stress while minimizing the volume of water used. We hereby define the position functions for irrigation UAVs based on an image of the Crop Water Stress Index (CWSI) of the crop. These trajectories suppose regular grid paths but they do not suppose constant speed. This methodology consists on dividing the crop into segments according to the grid paths, where the UAV will move in a straight line, and then finding the position function for each segment. We do not make any assumptions on the speed, and the fact that it varies according to the water stress conditions of the crop is what allows for precision irrigation to be achieved. Simulation results have shown that significant amounts of water can be saved by applying this irrigation methodology.