  The magnetic helicities of the cycloidal ordering in EuIrGe$_3$, with a
noncentrosymmetric tetragonal structure, have been studied by circularly
polarized resonant X-ray diffraction. It is shown that the helicity of each
cycloidal domain is uniquely determined and satisfies the symmetry relations of
the $C_{4v}$ point group of the crystal structure. The result shows that the
cycloidal helicity is determined by the Dzyaloshinskii-Moriya type
antisymmetric exchange interaction. The domain selection and the phase
transition by the external magnetic field along [100] and [110] have also been
studied. It is shown that the cycloidal plane prefers to be perpendicular to
the field and the transverse conical state is realized.
