Radiocarbon measurements can be used to deduce the proportion of renewable to fossil carbon in materials. While these biofraction measurements are performed routinely on solid and liquid substances, measurements of gaseous samples, such as methane, are still scarce. As a pioneering effort, we have developed a field-capable sampling system for the selective capture of CH4 for radiocarbon-concentration measurements. The system allows for biofraction measurements of methane by accelerator mass spectrometry. In environmental research, radiocarbon measurements of methane can be used for fingerprinting different sources of methane emissions. In metrology and industry, biofraction measurements can be utilized to characterize biogas/natural gas mixtures within gas-line networks. In this work, the portable sampling system is described in detail and reference measurements of biofractions of gaseous fuel samples are presented. Low-concentration (1-ppm-CH4) sampling for environmental applications appears feasible but has not been fully tested at present. This development allows for multitude of future applications ranging from Arctic methane emissions to biogas insertion to gas networks.