  Fast radio bursts (FRBs) are astrophysical transients of still debated
origin. So far several hundred events have been detected, mostly at
extragalactic distances, and this number is expected to grow significantly over
the next years. The radio signals from the burst experience dispersion as they
travel through the free electrons along the line-of-sight characterised by the
dispersion measure (DM) of the radio pulse. In addition, each photon also
experiences a gravitational Shapiro time delay while travelling through the
potentials generated by the large-scale structure. If the equivalence principle
(EP) holds, the Shapiro delay is the same for photons of all frequencies. In
case the EP is broken, one would expect an additional dispersion to occur which
could be either positive or negative for individual sources. Here we suggest to
use angular statistics of the DM fluctuations to put constraints on the EP
parametrized by the post-Newtonian parameter $\gamma$. Previous studies suffer
from the problem that the gravitational potential responsible for the delay
diverges in a cosmological setting, which our approach avoids. We carry out a
forecast for a population of FRBs observable within the next years and show
that any significant detection of the DM angular power spectrum will place
constraints on the EP that are by a few orders of magnitude more stringent than
current limits.
