A matching slot pair which radiates all the incident power in a circularly-polarised wave is proposed and analysed for use as a terminal in a leaky-wave slotted waveguide array. The position and size of the slots are numerically optimised to suppress reflection and to realise a desired polarisation in the tilted beam direction, which contributes to improving the antenna efficiency. It is verified experimentally that the return loss is below –15 dB over 0.1 GHz at the 4 GHz band and the 3 dB axial ratio bandwidth is about 5% in the tilted beam direction.