While there is still a lot to learn about astrocytes and their neuromodulatory role in the spatial and temporal integration of neuronal activity, their introduction to neuromorphic hardware is timely, facilitating their computational exploration in basic science questions as well as their exploitation in real-world applications. Here, we present an astrocytic module that enables the development of a spiking Neuronal-Astrocytic Network (SNAN) into Intel's Loihi neuromorphic chip. The basis of the Loihi module is an end-to-end biophysically plausible compartmental model of an astrocyte that simulates the intracellular activity in response to the synaptic activity in space and time. To demonstrate the functional role of astrocytes in SNAN, we describe how an astrocyte may sense and induce activity-dependent neuronal synchronization, switch on and off spike-time-dependent plasticity (STDP) to introduce single-shot learning, and monitor the transition between ordered and chaotic activity at the synaptic space. Our module may serve as an extension for neuromorphic hardware, by either replicating or exploring the distinct computational roles that astrocytes have in forming biological intelligence.