We propose a simple yet efficient scheme for a set of energy-harvesting sensors to establish secure communication with a common destination (a master node). An eavesdropper attempts to decode the data sent from the sensors to their common destination. We assume a single modulation scheme that can be implemented efficiently for energy-limited applications. We design a multiple-access scheme for the sensors under secrecy and limited-energy constraints. In a given time slot, each energy-harvesting sensor chooses between sending its packet or remaining idle. The destination assigns a set of data time slots to each sensor. The optimization problem is formulated to maximize the secrecy sum-throughput.