Current and next generations of radio surveys are expected to identify vast numbers of new sources, and as a result, identifying and classifying their morphologies will be a challenging task. Machine learning algorithms, such as a self-organising map (SOM), can be used to address this problem. We train a SOM on 251,259 multi-Gaussian sources from the Rapid ASKAP Continuum Survey (RACS), mapping them onto a grid of discrete neurons. We use Euclidean distance as a similarity metric to find the best-matching neuron or unit (BMU) for each input source. We label the neurons on the trained SOM grid based on observed morphologies and establish a reliability threshold by visually inspecting a sample of input images and their corresponding BMU. We find that sources with Euclidean distances of \(\lesssim \) 5 to their BMU (around 79 \(\%\) of sources) have an estimated reliability of \({>}90\%\) for their morphological labels. However, beyond Euclidean distances \(\gtrsim \) 7 it is unlikely that the morphological label accurately describes a given source. We export this information back to the RACS catalogue and create a value-added catalogue of complex sources with their SOM-derived morphological labels and a reliability percentage for the labels based on our validation process.