Just as a general rule to remember, transformables always rotate around its origin.
So, yes, as said above, if you want to rotate around its centre, its origin must be at its centre.
Indeed, all transformations are based around the origin: scale will scale outwards from its origin and setting its position technically sets where its origin will be (this means that you will likely need to reposition it after changing its origin - set its new position to where you want its centre to be, for example).