Unless I'm missing something we know very little about the orbital planes of individual systems.
Most exoplanetary systems (all of the transiting ones, whereas it is just a strong bias for the doppler-discovered planets) are discovered because they have high orbital inclination. This means that the planet's orbit takes it across the stellar disc as we view it. However, the entire arrangement can be rotated around the line of sight by any angle and this would give exactly the same observational signature.
That being the case, the only test I can immediately suggest is that if the planes of planetary systems were preferentially aligned with the galactic plane (ours isn't), then it would result in a lower planetary detection rate for stars in directions perpendicular to the Galactic plane in comparison with stars lying in the Galactic plane.
There may be some mileage in pursuing this, though I don't know of any results. For example the main Kepler field was directed just out of the Galactic plane, but the K2 fields are at a variety of Galactic latitudes along the ecliptic plane. If one could normalise somehow for the types of stars observed in each field and the differing data qualities then it might be possible to look at the "planetary occurrence rate" as a function of Galactic latitude.
The "all-sky" ground-based surveys are less suitable for this because they tend to avoid the Galactic plane because it is too crowded with targets.
The question can be more broadly addressed by looking at visual binary systems - i.e. those where you can resolve the components and study the orbit. There, it is possible to say something about the orbital planes of individual systems. A paper by Agati et al. (2015) has looked at this. They collected 51 systems with the requisite information, that are close to the Sun. They found only weak evidence for any anisotropy of the orbital poles and this weak alignment was closer to the ecliptic pole than the Galactic pole.
