The shape of a plant's root system influences its ability to reach essential nutrients in the soil and to acquire water during drought. Progress in engineering plant roots to optimize water and nutrient acquisition has been limited by our capacity to design and build genetic programs that alter root growth in a predictable manner. We developed a collection of synthetic transcriptional regulators for plants that can be compiled to create genetic circuits. These circuits control gene expression by performing Boolean logic operations and can be used to predictably alter root structure. This work demonstrates the potential of synthetic genetic circuits to control gene expression across tissues and reprogram plant growth.