Interesting question. I don't have any trials specifically about the anti-tank function of the Katyusha, but I do have some information that would allow us to extrapolate.

Let's split this question up into two parts. Part 1 is: can a rocket salvo hit a Tiger tank? A brigade of launchers armed with M-31 rocket launchers fires 1152 rockets in a salvo, covering a 1200x1000 m area. That's one rocket per a 33x33 m square. While infantry up to 400 meters away could be killed by the fragments, a direct or near direct hit would have to be scored on a Tiger to have a good chance of knocking it out. This is unlikely, even if we assume that the rockets will cluster more towards the center, rather than the edges of the zone under fire. The M-13 launcher brigade covers an 800x700 m area with 384 shells, which gives a worse figure of one rocket per a 38x38 meter square.

Now for part 2: in the unlikely event that a rocket strikes the top of a Tiger tank, what would happen to it? British trials showed that fragments from a 25-pounder shell exploding above a Tiger would damage its radiators to such a degree, that the tank would overheat and be forced to stop within five minutes. Direct impacts from 75 mm HE shells created fractures in the armour, and, in one case, even blew out a chunk.

Since the fragmentation from the Soviet rockets was much more impressive than the higher velocity (and therefore necessarily less brittle) 25-pounder shell, it's likely that the Tiger would be, at least, similarly damaged by a nearby explosion of a Katyusha rocket.

Sources:

P. Samsonov Katyusha Brigade

Armour Branch Report on Firing Trial against German Tiger Pz.Kw.VI.