Context. Integrated superconducting spectrometers (ISSs) for wide-band submillimeter (submm) astronomy use quasi-optical systems for coupling radiation from the telescope to the instrument. Misalignment in these systems is detrimental to the system performance. The common method of using an optical laser to align the quasi-optical components requires an accurate alignment of the laser to the submm beam from the instrument, which is not always guaranteed to a sufficient accuracy. Aims. We develop an alignment strategy for wide-band ISSs that directly uses the submm beam of the wide-band ISS. The strategy should be applicable in both telescope and laboratory environments. Moreover, the strategy should deliver similar quality of the alignment across the spectral range of the wide-band ISS. Methods. We measured the misalignment in a quasi-optical system operating at submm wavelengths using a novel phase and amplitude measurement scheme that is capable of simultaneously measuring the complex beam patterns of a direct-detecting ISS across a harmonic range of frequencies. The direct detection nature of the microwave kinetic inductance detectors in our device-under-test, DESHIMA 2.0, necessitates the use of this measurement scheme. Using geometrical optics, the measured misalignment, a mechanical hexapod, and an optimisation algorithm, we followed a numerical approach to optimise the positioning of corrective optics with respect to a given cost function. Laboratory measurements of the complex beam patterns were taken across a harmonic range between 205 and 391 GHz and were simulated through a model of the ASTE telescope in order to assess the performance of the optimisation at the ASTE telescope. Results. Laboratory measurements show that the optimised optical setup corrects for tilts and offsets of the submm beam. Moreover, we find that the simulated telescope aperture efficiency is increased across the frequency range of the ISS after the optimisation.