  Density fluctuations in the ionised interstellar medium have a profound
effect on radio pulsar observations, through angular scattering, intensity
scintillations, and small changes in time delays from dispersion. Here we show
that it is possible to recover the variations in dispersive delays that
originate from a dominant scattering region using measurements of the dynamic
spectrum of intensity scintillations, provided that the pulsar velocity and
scattering region location are known. We provide a theoretical framework for
the technique, which involves estimating the phase gradient from the dynamic
spectra and integrating that gradient to obtain phase variations. It can be
used to search for "extreme scattering events" (ESEs) in pulsars for which
precision dispersion delay measurements are not otherwise possible, or to
separate true dispersion variations from apparent variability caused by
frequency-dependent pulse shape changes. We demonstrate that it works in
practice by recovering an ESE in PSR J1603$-$7202, which is known from
precision dispersion delay measurements from pulsar timing. For this pulsar, we
find that the phase gradients also track the long-term variations in electron
column density observed by pulsar timing, indicating that the column density
variations and the scattering are dominated by the same thin scattering screen.
We identify a sudden increase in the scintillation strength and magnitude of
phase gradients over $\sim$days in 2010, indicating a compact structure. A
decrease in the electron density in 2012 was associated with persistent phase
gradients and preceded a period of decreased scintillation strength and an
absence of scintillation arcs.
