Electronic devices having moisture-insensitive optical touch sensors

An electronic device may have a touch sensitive display that is insensitive to the presence of moisture. An array of pixels in the display may be used to display images. A display cover layer may overlap the array of pixels. A light source may illuminate an external object such as a finger of a user when the object contacts a surface of the display cover layer. This creates scattered light that may be detected by an array of light sensors. The light source may supply light to an edge of the display cover layer at an angle that ensures total internal reflection within the display cover layer is sustained across the display cover layer even when the display cover layer is immersed in water or otherwise exposed to moisture.