The aviation sector contributes 3% of global CO2 emissions as it still relies heavily on fossil fuels. The use of low carbon hydrogen as a fuel, in both compressed or liquified forms, would drastically reduce its emissions. However, hydrogen has low volumetric energy density, and imposes a mass penalty due to storage tank requirements if used in compressed form. On the other hand, the liquefaction of hydrogen is energy-intensive and can consume ~40% of chemical energy stored in hydrogen. Ammonia, as a carbon-free hydrogen carrier, benefits from ease of storage and transport, and can be potentially used as an energy vector to enable advanced propulsion systems. Given the possibility of achieving zero-NOx in fuel cells, recent advances in fuel cell electric-powered aircraft, as well as fuel flexibility of Solid Oxide Fuel Cells (SOFCs), this work will explore the feasibility and challenges of direct ammonia-fed SOFCs as the power source for air aviation propulsion system. A model based on semi-empirical equations is developed for ammonia-powered fuel cells. A 130 kW general aviation case study is modelled and simulated in the paper to confirm the effectiveness and potential of the ammonia-powered fuel cell technology to be used as the next generation of propulsion systems in this size of aircraft. The comparative analyses demonstrated that the use of ammonia can decrease the mass of fuel consumed by 5.9% (in comparison with kerosene fueled aircraft) in a one-hour mission and allow achieving the emissions level targets set by Advisory Council for Aeronautics Research in Europe (ACARE) Flight Path 2050. Finally, the remaining practical challenges that need to be addressed to enable this important technology to be adopted by air vehicle manufacturers have been identified and discussed.