Self-drilling screws provide an efficient and cost-effective way of joining lightweight structural members. In this work, the performance of self-drilling screw connections for fiber-reinforced polymer (FRP) structural members is investigated, for use in joining panels or plates to square hollow sections (SHSs). To investigate the resistance to pullout loads, tensile tests were conducted on connection specimens consisting of an FRP plate joined to an FRP SHS at a right angle. The specimens were prepared in five configurations, with differences in pultrusion directions of the FRP plate, screw gauge size, and coarseness of the screw threads. The specimens having fibers oriented transversely in the FRP plate exhibited a flexural failure of the plate and the lowest connection strength. The specimens having fibers oriented longitudinally in the FRP plate failed by the screw being pulled out from the FRP SHS profiles; shearing out of the thread in the screw hole. An increase in screw gauge size and thread coarseness was found to be beneficial to the connection strength. Further analysis was carried out to estimate the initial stiffness and the connection strength, by finite-element and analytical modeling, respectively. In addition, these analyses are able to correlate the average shear stress at failure of the connection specimens to the screw gauge size, thread coarseness, and effective contact area of the screws.