A horn antenna is an extension of a rectangular waveguide. To feed the waveguide from a coaxial line you need a transition. Any good connector can be used, SMAs are good om DC to ~18 GHz.
\Designing a waveguide-to-coaxial transition is a complex task. This is why empirical designs are used, and a careful adjustment is needed. All that explains why good transitions are quite costly. You can try what is shown above but such design only works at one frequency or over a narrow band.
If you find a low-cost transition on e-bay and it works, be happy!