Monitoring wildfires has become increasingly critical due to the sharp rise in wildfire incidents in recent years. Optical satellites like Sentinel-2 and Landsat are extensively utilised for mapping burned areas. However, the effectiveness of optical sensors is compromised by clouds and smoke, which obstruct the detection of burned areas. Thus, satellites equipped with Synthetic Aperture Radar (SAR), such as dual-polarisation Sentinel-1 and quad-polarisation RADARSAT-1/-2 C-band SAR, which can penetrate clouds and smoke, are investigated for mapping burned areas. However, there is limited research on using compact polarisation (compact-pol) C-band RADARSAT Constellation Mission (RCM) SAR data for this purpose. This study aims to investigate the capacity of compact polarisation RCM data for burned area mapping through deep learning. Compact-pol m-χ decomposition and Compact-pol Radar Vegetation Index (CpRVI) are derived from the RCM Multi-Look Complex product. A deep-learning-based processing pipeline incorporating ConvNet-based and Transformer-based models is applied for burned area mapping, with three different input settings: using only log-ratio dual-polarisation intensity images, using only compact-pol decomposition plus CpRVI, and using all three data sources. The training dataset comprises 46,295 patches, generated from 12 major wildfire events in Canada. The test dataset includes seven wildfire events from the 2023 and 2024 Canadian wildfire seasons in Alberta, British Columbia, Quebec and the Northwest Territories. The results demonstrate that compact-pol m-χ decomposition and CpRVI images significantly complement log-ratio images for burned area mapping. The best-performing Transformer-based model, UNETR, trained with log-ratio, m-χ m-decomposition, and CpRVI data, achieved an F1 Score of 0.718 and an IoU Score of 0.565, showing a notable improvement compared to the same model trained using only log-ratio images (F1 Score: 0.684, IoU Score: 0.557). This is the first study to demonstrate that RCM C-band SAR data and its derived features are effective for burned area mapping.