We use on here, because the type of corner ( a street corner) does not have a significant 3rd dimension (height)-- it is merely two-dimensional, so that an object would be on it. Otherwise, to indicte directions we use on/at When I saw him, he was standing at/on the corner of that Street
If we are speaking of a box, room, or other enclosed object with a relatively significant vertical dimension, Or for indicating the position of something,
we use in:
The broom is in the corner of the room.
A vase stood in the corner of the room.