The moment of inertia of a semi circular Ring of mass M and Radius ‘R’ about an axis lying in the plane Which is passing through its centre and at an angle $\mathrm{\theta }$ With the line joining its ends

Consider another half of the ring making a complete a circular ring. Now, for whole ring, MOI along the axis will be: 

$I^{\mathrm{\prime }}=\frac{\left(2M\right)R^2}{2}$

So, for half (semi-circular) ring, the M.O.I about same axis will be:

$I=\frac{I^{\mathrm{\prime }}}{2}=\frac{M{R}^2}{2}$

so, MOI does not depend on the angle.