A sterile surgical drape for protecting a robotic surgical system includes an oblong drape of a clear flexible plastic material, which unfolds from a compact packet. From the proximal side of the main panel of the drape there project two pocket flaps, which are separated by a medial trough. The two pocket flaps are configured to slip over one another and together enclose the top of the control tower in an overlapping fashion, such that the robotic manipulator arms extend on either side of the main panel, while the camera/endoscope arm extends through the medial trough. The open ends of the pocket flaps are folded over to form cuffs, wherein a nurse can insert his/her hand to draw the flap over the top of the tower without touching non-sterile surfaces. The unfolding of the main panel is controlled by adhesive tabs or tear strips, so that the bottom of the panel does not engage the carts wheels or the floor.